The permiter of a triangle is 100 feet. the longest side is 3 feet less than twice the shortest side, and the third side is 7 feet longer than the shortest side. find the lengths of the sides of the triangle

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