Answer:
Smallest length side = 12 ft
Middle length side = 28 ft
Longest length side = 32 ft
Step-by-step explanation:
Perimeter of ∆ = sum of all its length sides
Thus, we are given that:
Perimeter = 72 ft
Let x represent the smallest length side. Therefore:
Smallest length side = x ft
Middle length side = (2x + 4) ft
Longest length side = (3x - 4) ft
Thus:
(2x + 4) + (3x - 4) + x = 72
Solve for x
2x + 4 + 3x - 4 + x = 72
Collect like terms
2x + 3x + x + 4 - 4 = 72
6x = 72
Divide both sides by 6
x = 72/6
x = 12
Find the length of all 3 sides by plugging in the value of x in each expression:
Smallest length side = x ft = 12 ft
Middle length side = (2x + 4) ft = (2(12) + 4) = 24 + 4 = 28 ft
Longest length side = (3x - 4) ft = (3(12) - 4) = (36 - 4) = 32 ft
