i do not understand

Question

 The length of the longer leg of a right triangle is 16 more than four times the length of the shorter leg. The length of the hypotenuse is 17 more than four times the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

Ok, so we need to set the length of the shortest leg, lets call it 'x'

 

the longer leg is 4x+16 and the hypotenuse is 4x+17

 

Now we need to use the Pythagorean theorem a^2+b^2= c^2

 

so 

 

x^2 + (4x+16)^2 = (4x+17)^2

 

if we expand that out we get 

 

x^2 +16 x^2 + 128x +  256 = 16 x^2 + 136 x + 289

 

doing a little canceling we get x^2 + 128x +256 = 136 X +289

 

it's quadratic, so we need to get everything onto one side so we get 

 

x^2 - 8x - 33 = 0

 

factor 

 

(x-11)(x+3)=0

 

so x = 11 or -3

 

but the side length cant be negative, so x = 11.

 

the sides are therefore 11, 60, and 61