Question

Determine the value of x for the triangle. show work.

Answer 1

x=5

Explanation:

x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.

Answer 2

5

Explanation:

Because this is a right triangle, you know that by the Pythagorean theorem:
`√((x+7)^2+x^2)=x+8`

Squaring both sides to get rid of the square root:

`(x+7)^2+x^2=(x+8)^2`

Expanding all of the parentheses:

`x^2+14x+49+x^2=x^2+16x+64`

Combine like terms:

`x^2-2x-15=0`

Factor:

`(x-5)(x+3)=0`

Since x cannot be negative, it is equal to 5. Hope this helps!