Question

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.

Answer 1

Answer: the length of the longest side is 14 inches

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