One leg of a right triangle is 2 cm more than twice the length of the other leg. The hypotenuse is 13 cm long.

Question

Algebraically determine the lengths of the triangle.

Answer 1

Let x = length of shorter leg

 

Then 2x+2 = length of longer leg

 

By the Pythagorean Theorem, x² + (2x+2)² = 13²

 

x² + 4x² + 8x + 4 = 169

 

5x² + 8x - 165 = 0

 

(5x + 33)(x - 5) = 0

 

x = -33/5 or x = 5

 

Since x can't be negative, x = 5      2x+2 = 12