In a right triangle, the measures of the legs are x and x + 14 and the measure of the hypotenuse is x + 16. Find the measure of x.

Question

asked May 14, 2022 167k views

1 Answer

HyeEun · Answer 1 · 2022-05-19T01:01:14+0000

Answer:

x=10

Explanation:

We can use the Pythagorean Theorem:

a^2+b^2=c^2

The two legs are x and (x + 14) and the hypotenuse is (x + 16). Therefore:

(x)^2+(x+14)^2=(x+16)^2

Expand:

$\displaystyle x^2+(x^2+28x+196)=x^2+32x+256$

Combine like terms:

2x^2+28x+196=x^2+32x+256

Subtract the right from the left:

(2x^2+28x+196)-(x^2+32x+256)=0

Subtract:

x^2-4x-60=0

Factor:

(x-10)(x+4)=0

Zero Product Property:

$x-10=0\text{ or } x+4=0$

Solve:

$\displaystyle x = 10 \text{ or } x = -4$

The x cannot be negative since a side cannot measure -4. So, our only answer is:

x=10

So, the legs are 10 and 24 with the hypotenuse being 26.