Question

A flower bed is in the shape of a triangle with oneside twice the length of the shortest side and thethird side is 12 feet more than the length of theshortest side. Find the dimensions if the perimeteris 180 feet.XWhat is the length of the shortest side?The length of the shortest side is57What is the length of the second side?The length of the second side isWhat is the length of the third side?The length of the third side is

Answer 1

Let's define the lengths of the triangle here.

1. x = shortest side

2. 2x = the length of the second side (twice the length of the shortest side)

3. x + 12 = the length of the third side

Another given information in the problem is that perimeter of the triangle = 180 feet.

Perimeter is the total length of all sides. Hence, we can say that x + 2x + x + 12 = 180 feet. From this, we can solve for x.

`\begin{gathered} x+2x+x+12=180 \\ \text{Add similar terms.} \\ 4x+12=180 \\ Subtract\text{ 12 on both sides of the equation.} \\ 4x+12-12=180-12 \\ 4x=168 \\ \text{Divide both sides by 4.} \\ x=42 \end{gathered}`

Hence, the length of the shortest side is 42 ft.

The length of the second side is 2 x 42 = 84 ft.

The length of the third side is 42 + 12 = 54 ft.