Question

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

Answer 1

Answer:

x=5

Step-by-step 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

Answer:

5

Step-by-step explanation:

Because this is a right triangle, you know that by the Pythagorean theorem:$\sqrt{(x+7)^2+x^2}=x+8$

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!