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Find the area of a right angle triangle whose base is 12 inches.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the area of a right angle triangle whose base is 12 inches.1. The...
Base = 12 inches.
In statement 1, hypotenuse = 13 inches. Using Pythagorean theorem, we have height = √(13² - 12²) = 5.
Area = 1/2 × 5 × 12 = 30 square inches. The statement is sufficient.
In statement 2, perpendicular height = 1/2 (base) - 1 = 1/2 × 12 -1 = 5 inches. Base = 12 inches.
Area =1/2 × 5 × 12 = 30 square inches. The statement is sufficient.
In statement 1, hypotenuse = 13 inches. Using Pythagorean theorem, we have height = √(13² - 12²) = 5.
Area = 1/2 × 5 × 12 = 30 square inches. The statement is sufficient.
In statement 2, perpendicular height = 1/2 (base) - 1 = 1/2 × 12 -1 = 5 inches. Base = 12 inches.
Area =1/2 × 5 × 12 = 30 square inches. The statement is sufficient.
Most Upvoted Answer
Find the area of a right angle triangle whose base is 12 inches.1. The...
Statement 1: The hypotenuse is 13 inches.
Statement 2: The perpendicular height of the triangle is one less than half its base.
To find the area of a right-angled triangle, we need to know the length of the base and the height (perpendicular to the base). Let's evaluate each statement separately:
Statement 1: The hypotenuse is 13 inches.
Knowing the length of the hypotenuse alone is not enough to determine the area of the triangle. The hypotenuse only provides information about the length of the sides, not the height or the angles of the triangle. Therefore, statement 1 alone is not sufficient.
Statement 2: The perpendicular height of the triangle is one less than half its base.
Let's denote the base of the triangle as 'b' inches. According to statement 2, the height of the triangle is (1/2)b - 1 inches.
To calculate the area of the triangle, we need both the base and the height. Therefore, statement 2 alone is sufficient to determine the area of the triangle.
Using both statements:
Now, if we consider both statements together, we have the length of the base (12 inches) from statement 2 and the length of the hypotenuse (13 inches) from statement 1.
We can use the Pythagorean theorem to find the height of the triangle, which is the missing piece of information needed to calculate the area.
By the Pythagorean theorem:
base^2 + height^2 = hypotenuse^2
12^2 + height^2 = 13^2
144 + height^2 = 169
height^2 = 169 - 144
height^2 = 25
height = 5
Now, we have the base (12 inches) and the height (5 inches), so we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Therefore, both statements together are sufficient to determine the area of the triangle.
Hence, the answer is option C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statement 2: The perpendicular height of the triangle is one less than half its base.
To find the area of a right-angled triangle, we need to know the length of the base and the height (perpendicular to the base). Let's evaluate each statement separately:
Statement 1: The hypotenuse is 13 inches.
Knowing the length of the hypotenuse alone is not enough to determine the area of the triangle. The hypotenuse only provides information about the length of the sides, not the height or the angles of the triangle. Therefore, statement 1 alone is not sufficient.
Statement 2: The perpendicular height of the triangle is one less than half its base.
Let's denote the base of the triangle as 'b' inches. According to statement 2, the height of the triangle is (1/2)b - 1 inches.
To calculate the area of the triangle, we need both the base and the height. Therefore, statement 2 alone is sufficient to determine the area of the triangle.
Using both statements:
Now, if we consider both statements together, we have the length of the base (12 inches) from statement 2 and the length of the hypotenuse (13 inches) from statement 1.
We can use the Pythagorean theorem to find the height of the triangle, which is the missing piece of information needed to calculate the area.
By the Pythagorean theorem:
base^2 + height^2 = hypotenuse^2
12^2 + height^2 = 13^2
144 + height^2 = 169
height^2 = 169 - 144
height^2 = 25
height = 5
Now, we have the base (12 inches) and the height (5 inches), so we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Therefore, both statements together are sufficient to determine the area of the triangle.
Hence, the answer is option C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
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Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?
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Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Find the area of a right angle triangle whose base is 12 inches.1. The hypotenuse is 13 inches.2. The perpendicular height of the triangle is one less than half its base.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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