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Directions: Solve the problem and select the best of the answer choices given.
A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?
- a)(z – 4)2 = z2 – (z - 2)2
- b)(z – 2)2 = (z – 4) – z2
- c)z2 + 42 + 22 = 62
- d)(z – 2)2 = z2 – (z - 1)2
- e)(z + 2)2 + (z + 4)2 = z2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Directions: Solve the problem and select the best of the answer choice...
The correct response is (A). If we know the longest side is “z,” we can label the other two sides as “z-4” and “z-2” respectively because we know that “consecutive even” means each side differs from its next-largest neighbor by 2. For example: 6, 8, 10.
We would use the Pythagorean Theorem to find the value of z:
a2 + b2 = c2
(z – 2)2 + (z – 4)2 = z2
a2 + b2 = c2
(z – 2)2 + (z – 4)2 = z2
Remember that “c” is always the hypotenuse, or the longest side. Only choice (A) matches this equation.
Most Upvoted Answer
Directions: Solve the problem and select the best of the answer choice...
The correct response is (A). If we know the longest side is “z,” we can label the other two sides as “z-4” and “z-2” respectively because we know that “consecutive even” means each side differs from its next-largest neighbor by 2. For example: 6, 8, 10.
We would use the Pythagorean Theorem to find the value of z:
a2 + b2 = c2
(z – 2)2 + (z – 4)2 = z2
a2 + b2 = c2
(z – 2)2 + (z – 4)2 = z2
Remember that “c” is always the hypotenuse, or the longest side. Only choice (A) matches this equation.
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Community Answer
Directions: Solve the problem and select the best of the answer choice...
The longest side of a right triangle is always the hypotenuse. In a right triangle with consecutive even integers as sides, we can represent the sides as x, x+2, and x+4 (since consecutive even integers are always 2 units apart).
To find the hypotenuse (z), we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
Using this information, we can set up the equation:
(x)^2 + (x+2)^2 = (x+4)^2
Expanding and simplifying:
x^2 + (x^2 + 4x + 4) = x^2 + 8x + 16
Combining like terms:
2x^2 + 4x + 4 = x^2 + 8x + 16
Moving all terms to one side:
x^2 - 4x - 12 = 0
Now, we can solve this quadratic equation to find the possible values of x, which will give us the possible values of z.
Therefore, the correct equation that could be used to find z is:
c) x^2 - 4x - 12 = 0
To find the hypotenuse (z), we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
Using this information, we can set up the equation:
(x)^2 + (x+2)^2 = (x+4)^2
Expanding and simplifying:
x^2 + (x^2 + 4x + 4) = x^2 + 8x + 16
Combining like terms:
2x^2 + 4x + 4 = x^2 + 8x + 16
Moving all terms to one side:
x^2 - 4x - 12 = 0
Now, we can solve this quadratic equation to find the possible values of x, which will give us the possible values of z.
Therefore, the correct equation that could be used to find z is:
c) x^2 - 4x - 12 = 0
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Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer?
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Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer?.
Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Solve the problem and select the best of the answer choices given.A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?a)(z – 4)2 = z2 – (z - 2)2b)(z – 2)2 = (z – 4) – z2c)z2 + 42 + 22 = 62d)(z – 2)2 = z2 – (z - 1)2e)(z + 2)2 + (z + 4)2 = z2Correct answer is option 'A'. Can you explain this answer?.
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