In a triangle, the longest side is 8 units more than the shortest side, and the shortest side is half the remaining side. Find the length of the longest side if the triangle's perimeter is 32 units.

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

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