how long should the sides of the triangle be?

Question

a toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. how long should the sides of the triangle be?

Answer 1

Let the shorter leg be denoted by x. then longer leg is x+6 and the hypotenuse is x+12. By using Pythagoras theorem, 

 

x²+(x+6)²= (x+12)²

 

x²+x²+12x+36 = x²+24x+144

 

Rearranging,

 

x²-12x-108 = 0

 

108 = 3*3*3*2*2 (prime factors). It can be easily seen that -18 and 6 will add unto -12 (coefficient of x) and product gives -108.

 

therefore, the equation becomes

 

(x-18)(x+6) = 0

 

We get solutions of 18 and -6. Since physical lengths cannot be negative, we have the solution to be 18 for x which is the shorter leg.

 

So the lengths are 18, 24, 30. Here hypotenuse is 30.

 

Check:

 

18²+24²=324+576 = 900 = 30²