Right Triangle

Question

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 8 cm more than the shorter leg and the hypotenuse 16 cm more than the shorter leg. How long should the sides of the triangle be?

Answer 1

Let x represent the shorter leg.  This means that the longer leg will be (x+8) and the hypotenuse will be (x+16).

 

Use Pythagorean theorem to calculate possible values for x:

 

x² + (x+8)² = (x+16)²

 

expand:

 

x² + (x+8)(x+8) = (x+16)(x+16)

 

FOIL (multiply the expressions in parentheses)

 

x² + x² + 16x +64 = x² + 32x + 256

 

Combine like terms:

 

2x² + 16x + 64 = x² + 32x + 256

 

Subtract the terms from the right side (to have the whole equation equal zero):

 

2x² - x² + 16x - 32x + 64 - 256 = 0

 

Combine like terms:

 

x² -16x - 192 = 0

 

Factor left side:

 

(x - 24)(x + 8) = 0

 

Set each part on left side equal to zero and solve:

 

x - 24 = 0            x + 8 = 0

x = 24               x=-8

 

Since x should not be a negative value (no negative centimeters), the -8 value is not valid.  Substitute 24 back into original triangle values (at top of page) and you will have sides of 24, 32, and 40.