SOLUTION: a lot is in the shape of a triangle. The hypotenuse is 3 m longer than the longer leg. The longer leg is 6 m longer than twice the length of the shorter leg. Find the perimeter of

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let s = shortest leg
let l=longest leg = 2s+6
let h = hypt = l+3= (2s+6) +3 = 2s +9
hypt also allows right triangle therefore use pythagorous
c^2 = a^2 +b^2
(2s+9)^2= s^2 +(2s+6)^2
4s^2 + 36s +81 = s^2 + ( 4S^2 +24s +36)
collect like terms
0= s^2 -12s-45
factor
0= ( s+3) (s-15)
s= (-3) not possible
and s= (15)
check
triangle is 15 - 36 - 39 and pythagorous confirms ok
and finally per = 15+36+39 = 90