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x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

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x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

by Max@Math Revolution » Thu Mar 05, 2020 2:19 am

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[GMAT math practice question]

x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

A. 2
B. 3
C. 4
D. 5
E. 6
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Re: x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

by Scott@TargetTestPrep » Sat Mar 07, 2020 6:32 am
Max@Math Revolution wrote: ↑
Thu Mar 05, 2020 2:19 am
 [GMAT math practice question]

x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

A. 2
B. 3
C. 4
D. 5
E. 6
Solution:

Since 3^2 + 4^2 = 5^2, the value of x must be 3.

Alternate Solution:

Let’s use the Pythagorean theorem, noting that the hypotenuse must be the longest side, x + 2.

x^2 + (x + 1)^2 = (x + 2)^2

x^2 + x^2 +2x + 1 = x^2 + 4x + 4

2x^2 + 2x + 1 = x^2 + 4x + 4

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 OR x = -1

Since x is a length, it must be positive, so x = 3.


Answer: B

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Re: x, x+1, and x+2 denote the lengths of the sides of a right triangle. What is the value of x?

by Max@Math Revolution » Sun Mar 08, 2020 6:20 pm
=>

We have
(x + 2)^2 = (x + 1)^2 + x^2
x^2 + 4x + 4 = x^2 + 2x + 1 + x^2
x^2 + 4x + 4 = 2x^2 + 2x + 1
x^2 – 2x -3 = 0
or (x - 3)(x + 1) = 0.
Thus, we have x = 3 since x is positive.

Therefore, B is the answer.
Answer: B
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