The longest side of a triangle is 5 inches. Longer than the shortest side. The medium side is 4 inches. Longer than the shortest side. If the perimeter of the triangle is 24 inches, what are the lengths of the three sides?

The answer to your question is L = 10 in , M = 9 in ; S = 5 in

Step-by-step explanation:

Data

longest side = 5 + x in

medium side = 4 + x in

shortest side = x

Perimeter = 24 in

Process

1.- Write and equation to solve this problem

    Perimeter = longest side + medium side + shortest side

Substitution

             24 = (5 + x) + (4 + x) + x

Simplification

            24 = 5 + x + 4 + x + x

            24 = 9 + 3x

            24 - 9 = 3x

                  15 = 3x

                   x = 15/3

                   x = 5

2.- Calculate the lengths of the side

Longest side = 5 + 5 = 10 in

Medium side = 5 + 4 = 9 in

Shortest side = 5 in

the shortest side is 5 inches.

The medium side is 9 inches.

The longest side is 10 inches

Step-by-step explanation:

Let x represent the length of the shortest side.

Let y represent the length of the medium side.

Let z represent the length of the longest side.

The longest side of a triangle is 5 inches longer than the shortest side. This means that

z = x + 5

The medium side is 4 inches longer than the shortest side. This means that

y = x + 4

If the perimeter of the triangle is 24 inches, it means that

x + y + z = 24 - - - - - - - - - - - - - -1

Substituting z = x + 5 and y = x + 4 into equation 1, it becomes

x + x + 4 + x + 5 = 24

3x + 9 = 24

3x = 24 - 9 = 15

x = 15/3 = 5

y = x + 4 = 5 + 4

y = 9

z = x + 5 = 5 + 5

z = 10