Question

A right triangle has base (x - 7) units and height (2x - 10) units.

Part A: What is the square of the length of the hypotenuse of the triangle? Show your work.

Answer 1

@Hero

Answer 2

In general when you have a right triangle, a and b are considered the side lengths and c is considered the hypotenuse. The pythagorean theorem is an equation that relates all three sides together:

a^2 + b^2 = c^2

Where c^2 is the square length of the hypotenuse. In this case, we can say that

a = the height of the right triangle = 2x - 10
b = the base of the right triangle = x - 7

Therefore the square length of the hypotenuse is represented by:
(2x - 10)^2 + (x - 7)^2 = c^2

Basically what you want to do is expand the left side completely to find the appropriate expression for c^2