If x-1, x+6, x+7 are 3 side lengths of a right triangle, what is the v

Question

If x-1, x+6, x+7 are 3 side lengths of a right triangle, what is the value of x?
 
 A. 4 B. 5 C. 6 D. 7 E. 8

Abhishek009 · Answer

( x + 7 )^2 = ( x - 1 )^2 + ( x + 6 )^2

So,  (x^2 + 14x + 49 ) = ( x^2 - 2x + 1 ) +( x^2 + 12x + 36 )

Or,  x^2 + 14x + 49 = 2x^2 +10x + 37

Or,  4x + 12 = x^2

Or,  x^2 - 4x - 12 = 0

Or,  ( x + 2 ) ( x - 6 ) = 0

So,  x = -2 & 6

Hence, The value of x is (C) 6

PS : Knowledge of    Pythagorean triple    can also cme handy for solving such question , without using Quadratic Equatiop form...

souvonik2k · Answer

This problem is a good example of plugin the answers.
Plugging in the answers for x, we see that only C satisfies the pythagorean triplet

ScottTargetTestPrep · Answer

Since we are given a right triangle, the length of the sides must satisfy the Pythagorean Theorem, which states that the sum of the squares of the two legs is equal to the square of hypotenuse. x + 7 must be length of the hypotenuse because it has the largest value when compared to x - 1 and x + 6, which means x - 1 and x + 6 are the lengths of the two legs. Therefore, we can create the following equation:

(x - 1)^2 + (x + 6)^2 = (x + 7)^2

x^2 - 2x + 1 + x^2 + 12x + 36 = x^2 + 14x + 49

2x^2 + 10x + 37 = x^2 + 14x + 49

x^2 - 4x - 12 = 0

(x - 6)(x + 2) = 0

x = 6 or x = -2

If x = -2, then x - 1 = -3. However, since x - 1 is a side length of a triangle, it can’t be negative, so x can’t be -2.

Thus, x must be 6, and our sides of the triangle are:

6 - 1 = 5

6 + 6 = 12

6 + 7 = 13

Answer: C

MathRevolution · Answer

==> (x-1)^2+(x+6)^2=(x+7)^2, x^2-2x+1+x2+12x+36=x^2+14x+49.
From x^2-4x-12=0 to (x-6)(x+4)=0, x=6, since -4 does not work, you get x=6.
Therefore, the answer is C.
Answer: C

bumpbot · Answer

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If x-1, x+6, x+7 are 3 side lengths of a right triangle, what is the v

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If x-1, x+6, x+7 are 3 side lengths of a right triangle, what is the v

Prep Toolkit

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My Rewards