Algebra Help

Question

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 2 cm more than the shorter leg and the hypotenuse 4 cm more than the shorter leg. How long should the sides of the triangle be?

Answer 1

use the Pythagorean Theorem

(x+4)^2=x^2+(x+2)^2

x^2+8x+16=x^2+x^2+4x+4

x^2+8x+16=2x^2+4x+4

2x^2+4x+4-x^2-8x-16=0

x^2-4x-12=0

factor

(x-6)(x+2)=0

x-6=0

x=6 cm

x+2=8 cm

x+4=10 cm

Answer 2

let s be the shortest side of the right triangle.  The sides are s,  s + 2 and s + 4

 

Use the Pythagorean theorem to solve.

 

s² + (s + 2) ² = ( s + 4 )² ; foil 

2s² + 4s + 4 = s² + 8s + 16; combine like terms

s² - 4s - 12 = 0 ; factor

( s-6) (s +2) = 0

Therefore, s is 6, or -2.

-2 is not sensible so the shorter side is 6 cm. The hypotenuse is 10 and the longer side 8.