Algebra 1 help please

Question

Find the lengths of each side of the following right triangles. Show all calculations. 

 

1. In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg.

 

Short leg =_?  Long leg =_?  Hypotenuse=_?

Answer 1

S² + L² = H²

S = L - 6

L = H - 6

S = H - 6 - 6 = H - 12

(H-12)² + (H-6)² = H²

Solve for H

Answer 2

let x= short leg (a),  so x+6 = long leg (b) and x+6+6 = hypotenuse (c)

 

c² = a² + b^{2    ==>}  short leg (a)=18, long leg (b) = a+6 = 24 and hypotenuse (c) = a+6+6 = 30