need help solving this problem, please.

Question

The shorter leg of a right triangle is 9ft
shorter than the longer leg. The hypotenuse is 9ft
longer than the longer leg. Find the side lengths of the triangle.

Answer 1

The stated information can be summarized as follows:

short leg = x - 9

long leg = x

hypotenuse = x+9

 

Using the Pythagorean theorem, (x+9)² = (x-9)² = x²

 

Squaring the binomial properly, we obtain x²+18x+19 = x²-18x+81 + x²

 

Simplifying, we get 0 = x² - 36x and factoring yields x(x-36) = 0.  our only acceptable answer is x = 36.

 

The three sides are of length 27, 36 and 45 ft each; this is similar to a 3-4-5 triangle.

 

To conclude philosophically, USE ALGEBRA!