Length of shorter leg of triangle

Question

Find the length of a right triangle if the longer leg is 10 feet more than the shorter leg and the hypotenuse is 10 feet less than twice the shorter length 

Answer 1

Let x = length of shorter leg

 

Then x + 10 = length of longer leg and 2x - 10 = length of hypotenuse

 

By the Pythagorean Theorem, x² + (x+10)² = (2x-10)²

 

Simplifying, we have x² + x² + 20x + 100 = 4x² - 40x + 100

 

                                            2x² + 20x = 4x² - 40x

 

                                                       0 = 2x² - 60x

 

                                                                  0 = 2x(x-30)

 

x = 0 or 30

 

Since x can't be 0, x = 30 ft

 

Length of shorter leg = x = 30 ft

Length of longer leg = x + 10 = 40 ft

length of hypotenuse = 2x - 10 = 50 ft