Just use the Pythagorean Theorem and a letter. This right triangle has a shorter leg s, a longer leg l, and a hypotenuse h. The Pythagorean theorem says
s2 + l2 = h2
According to the question
l = 2s + 20
h = 2s + 22 so...
s2 + (2s + 20)2 = (2s + 22)2
s2 + 4s2 + 80s + 400 = 4s2 + 88s + 484
s2 - 8s - 84 = 0
(s - 14)(s + 6) = 0
s = 14, -6
Actually, only one of these is the length of the shorter leg. Which one? And how long are the longer leg and hypotenuse?
Andrew M.
11/20/17