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What is the height of the triangle?
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the height of the triangle?I. The area of the triangle is 20 t...
I. A = 20 x B ½ x B x H = 20 x B
⇒ H = 40.
∴ I alone gives the answer.
II gives the perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
∴ Correct answer is (a).
⇒ H = 40.
∴ I alone gives the answer.
II gives the perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
∴ Correct answer is (a).
Most Upvoted Answer
What is the height of the triangle?I. The area of the triangle is 20 t...
To find the height of a triangle, we need either the length of the base and the area, or the lengths of two sides of the triangle. Let's analyze each statement given in the question:
Statement I: The area of the triangle is 20 times its base.
Statement II: The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
Statement I alone is sufficient to answer the question. Here's why:
If we know the area of a triangle and the length of its base, we can find its height using the formula: Area = (1/2) * base * height. Given that the area is 20 times the base, we can express this relationship as: Area = 20 * base. Plugging this into the formula, we get: 20 * base = (1/2) * base * height. Simplifying this equation, we find: height = 40.
Therefore, statement I alone is sufficient to determine the height of the triangle.
Statement II alone is not sufficient to answer the question. Here's why:
Knowing the perimeter of a triangle does not provide any information about its height. The perimeter is the sum of the lengths of all three sides of the triangle, and there are infinitely many triangles with different heights that can have the same perimeter as a square of side 10 cm. Therefore, statement II alone does not give us enough information to determine the height of the triangle.
In conclusion, statement I alone is sufficient to answer the question, while statement II alone is not. Therefore, the correct answer is option 'A'.
Statement I: The area of the triangle is 20 times its base.
Statement II: The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
Statement I alone is sufficient to answer the question. Here's why:
If we know the area of a triangle and the length of its base, we can find its height using the formula: Area = (1/2) * base * height. Given that the area is 20 times the base, we can express this relationship as: Area = 20 * base. Plugging this into the formula, we get: 20 * base = (1/2) * base * height. Simplifying this equation, we find: height = 40.
Therefore, statement I alone is sufficient to determine the height of the triangle.
Statement II alone is not sufficient to answer the question. Here's why:
Knowing the perimeter of a triangle does not provide any information about its height. The perimeter is the sum of the lengths of all three sides of the triangle, and there are infinitely many triangles with different heights that can have the same perimeter as a square of side 10 cm. Therefore, statement II alone does not give us enough information to determine the height of the triangle.
In conclusion, statement I alone is sufficient to answer the question, while statement II alone is not. Therefore, the correct answer is option 'A'.
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What is the height of the triangle?I. The area of the triangle is 20 times its base.II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.a)I alone sufficient while II alone not sufficient to answerb)II alone sufficient while I alone not sufficient to answerc)Either I or II alone sufficient to answerd)Both I and II are not sufficient to answerCorrect answer is option 'A'. Can you explain this answer?
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