Answer: the length of the longest side is 14 inches
Step-by-step explanation:
Let x represent the length of the shortest side.
Let y represent the length of the medium(remaining) side.
Let z represent the length of the longest side.
In a triangle, the longest side is 8 units more than the shortest side. It means that
z = x + 8
The shortest side is half the remaining side. This means that
x = y/2
y = 2x
if the triangle's perimeter is 32 units, it means that
x + y + z = 32- - - - - - -- - - - -1
Substituting z = x + 8 and y = 2x into equation 1, it becomes
x + 2x + x + 8 = 32
4x + 8 = 32
4x = 32 - 8 = 24
x = 24/4
x = 6
y = 2 × 6 = 12
z = 6 + 8 = 14
