The shortest side of a triangle measures 15 inches less than the longest side. If the third side is 2 inches shorter than the longest side and the perimeter is 103 inches, find the measure of the 3 sides.

Step-by-step explanation:

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

The shortest side of a triangle measures 15 inches less than the longest side. It means that the length of the shortest side is x - 15.

If the third side is 2 inches shorter than the longest side, it means that the length of the third 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 103 inches. It means that

x + x - 15 + x - 2 = 103

3x - 17 = 103

3x = 103 + 17 = 120

x = 120/3

x = 40

The length of the longest side is

40 inches

The length of the third side is

40 - 2 = 38 inches

The length of the shortest side is

40 - 15 = 25 inches