Answer:

Let s = the length of the shorter leg.

The length of the longer leg is 7 + s.

The length of the hypotenuse is 2s - 7.

Use the Pythagorean Theorem.

s2 + (7 + s)2 = (2s - 7)2 ... Now square the binomials to get:

s2 + 49 + 14s + s2 = 4s2 - 28s + 49 ... Combine like terms and reorder them in descending power to get:

2s2 + 14s + 49 = 4s2 - 28s + 49 ... Subtract 2s2 from both sides and subtract 49 from both sides to get: 

42s = 2s2 ... Divide both sides by s to get:

42 = 2s ... Divide both sides by 2 to get:

21 = s

The shorter leg is 21 meters long.