One leg of a right triangle is 1in more than twice the other leg. the hypotenuse is square root 29 in long. Find the lengths of the legs.

Question

The answer is 2 inches and 5 inches. Not sure how to set this up.

Answer 1

Let the lengths of the legs be a and 2a+1. By Pythagoras 29=a^2+4a^2+4a+1=5a^2+4a+1.

5a^2+4a-28=0=(5a+14)(a-2), so a=2 or -14/5. The negative root can be rejected because we cannot have a negative side length. So a=2 and 2a+1=5 (25+4=29).