The perimeter of a triangle is 24inches. The longest side is 4 more than the middle side, and the smallest side is half the length of middle side. What are the lengths?

Step-by-step explanation:

the length of the smallest side is 4 inches.

the length of the middle side is 8 inches.

the length of the longest side is 12 inches.

Step-by-step explanation:

Let x represent the length of the middle side of the triangle.

The longest side is 4 more than the middle side. It means that the length of the middle side is x + 4.

The smallest side is half the length of middle side. It means that the length of the smallest side is

x/2

The formula for determining the perimeter of a triangle is

Perimeter = a + b + c

Where a, b and c are the lengths of each side of the triangle. The perimeter of the triangle is 24 inches. It means that

x + 4 + x + x/2 = 24

Multiplying both sides of the equation by 2, it becomes

2x + 8 + 2x + x = 48

5x = 48 - 8

5x = 40

x = 40/5

x = 8 inches

The length of the longest side is

8 + 4 = 12 inches

The length of the smallest side is

8/2 = 4 inches