The length of the longer leg of a right triangle is 6ft more than twice the length of the shorter leg.

Question

 The length of the hypotenuse is 9ft more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

A right triangle tells use that we can use Pythagorean theorem.

 

Let the shorter leg = x

Let the longer leg = 2x + 6

Let the hypotenuse = 2x + 9

 

Apply the theorem to the variables to write an equation.  Then solve for x.

 

x² + (2x + 6)² = (2x + 9)²

 

x² + (2x + 6)(2x + 6) = (2x + 9)(2x + 9)

 

x² + 4x² + 24x + 36 = 4x² + 36x + 81

 

 

Make the right side equal to zero.

 

x² - 12x - 45 = 0

 

 

Factor the left side using FOIL.

 

(x - 15)(x + 3) = 0

 

 

Set the factors equal to zero.

 

x - 15 = 0             and                 x + 3 = 0

 

x = 15                                        x = -3

 

 

Since we cannot have a negative value for dimensions, we accept the positive value of x:

 

x = 15

 

 

This is also the length of the shorter leg.  Substitute this value of x to find the other side lengths.