A right triangle's medium side is 2 yards shorter than twice the length of its shortest side

Question

A right triangle's medium side is 2 yards shorter than twice the length of its shortest side. Its longest side is 7 yards shorter than 4 times the length of its shortest side. How long is the medium side of the triangle?

Answer 1

m=2s-2 = middle sized side

h=4s-7 = hypotenuse = longest side

s= shortest side

longest side of a right triangle = square root of the sum of the other two sides squared

h^2 = m^2 + s^2

(4s-7)^2 = m^2 + (2s-2)^2

16^2 - 56s + 49 = m^2 + 4s^2 -8s +4

m^2 = 12s^2 -48s +45

m = sqr(12s^2 -48s +45)

m=sqr[(6s-15)(2s-3)]