Triangles and Math

Question

One leg of a right triangle is 7 inches longer than the length of the other shorter leg. If the hypotenuse is 8 inches longer than the short leg, find the lengths of all the sides of the right triangle.

 

Please help me solve this and if you could explain how to do it, that would be great! Thanks!

Answer 1

Pythagorean theorem is a² + b² = c^2.

 

x² +  (x+7)² = (x+8)²

 

x² + x² + 14 x + 49= x² + 16x + 64

 

x2 -2x -15=0

 

(x+3) (x-5) = 0

 

x= -3  x= 5

 

Since x cannot be -, the answer is x=5

 

Therefore 5² + 12² = 13^2.. Therefore, the sides are 5, 12 and 13.