Question

A flower-bed is in the shape of a triangle with one side twice the length of the shortest side and the third side 15 feet longer than the shortest side. If the perimeter is 100 feet and if x represents the length of the shortest side, find an equation to solve for the lengths of the three sides.

Answer 1

The three sides are 21.25, 42.50, and 36.25 feet for a total of 100 feet.

Step-by-step explanation:

Let the side of the triangle with the shortest side be x.

One side is twice the length of the shortest side, so we can write the second side as 2x. The third side is 15 feet longer than the shortest, so we can write x + 15 for the third side. We also find that the perimeter is 100 feet.

The perimeter of a triangle is the sum of its three sides, so lets write the sum of the three sides and set it equal to 100 feet:

x + 2x +(x + 15) = 100 feet

No solve for x:

4x + 15 = 100 feet

4x = 85 feet

x = 21.25 feet

The three sides are:

1) x = 21.25 feet

2) 2x = 42.50 feet

3) x+15 = 36.25 feet

The sum of these three lengths is 100 feet.