Question

Use the Pythagorean Theorem to find x.

Answer 1

11

Explanation:

The Pythagorean theorem states that in a right triangle,
`a^2+b^2 = c^2` , where c is the hypotenuse, and a and b are the legs. So to use the Pythagorean theorem, we let
`a=x-3,b=x+4` and
`c=x+6`. Expanding everything gives
`2x^2+2x+25=x^2+12x+36`

Moving everything to one side tells us

`x^2-10x-11=0`

So

`(x-11)(x+1)=0`

This means that either x = 11 or x = -1. But looking back at our equation, x = -1 is a false solution, because sides of a triangle could not be negative in length, and x-3 = -4 when x =-1. Therefore x = 11.