let the shortest side be 's'
longest side be ' l '
and the third side be ' t'
P = s + l + t
P = 100
l - 3 = 2s
l = 2s + 3--- the longest side is 3 feet less than twice the shortest side
t= 7 + s ---- the third side is 7 feet longer than the shortest side
sub in (2s + 3) for l and (7 + s) for t
P = s + l + t
P = s + 2s + 3 + 7 + s
P = 100
100 = s + 2s + 3 + 7 + s
100 = 4s + 10
4s = 100 - 10
4s = 90
s = 90/4
s = 22.5
P = s + l + t
100 = 22.5 + l + t
100 - 22.5 = l + t
77.5 = l + t
from the previous equation we know l = 2s + 3
we'll plug in l into 77.5 = l + t
77.5 = 2s + 3 + t
we know s = 22.5
77.5 = 2(22.5) + 3 + t
77.5 = 48 + t
t = 77.5 - 48
t = 29.5
l = 2s + 3
l = 2(22.5) + 3
l = 48
the lengths are 22.5, 29.5 and 48
