Math, pythagorean theorem

Question

The longer leg of a right triangle is 7CM longer than the shorter leg. The hypotenuse is 9CM longer than the shorter leg. Find the side legs of the triangle.

Answer 1

Let x be the length of the shorter leg

The the length of the longer leg will be x+7

The the length of the hypotenuse will be x+9

The pythagorean theorem is

c²=a²+b²

(x + 9)² = x² + (x + 7)²

 

x² + 18x + 81 = x² + (x² + 14x + 49)

 

x² - 4x - 32 = 0

 

(x - 8)(x + 4) = 0

x=8 and x=-4

but since we can not have a -4 length, the only answer will be

 

x = 8 cm

 

So the short leg will be 8 cm

long leg will be 8+7 =15 cm

hypotenuse will be 8+9= 17 cm