Question

A rectangular athletic field is twice as long as it is wide if the perimeter of the athletic field is 360 yards what are its dimensions. The width isThe length is

Answer 1

Step 1. We will start by making a diagram of the situation.

Since the length of the rectangle is twice the width, if we call the width x, then the length will be 2x as shown in the diagram:

Step 2. One thing that we know about the rectangle is its perimeter:

`\text{Perimeter}\longrightarrow360\text{yd}`

This perimeter has to be the result of the sum of all of the sides of the rectangle:

`x+x+2x+2x=360`

Step 3. Solve the previous equation for x.

In order to solve for x, the first step is to combine the like terms on the left-hand side:

`6x=360`

The second step to solve for x is to divide both sides of the equation by 6:

`(6x)/(6)=(360)/(6)`

Simplifying:

`x=60`

Step 4. Remember from the diagram from step 1, that x was the width of the rectangle:

`\text{width}\longrightarrow x\longrightarrow60yd`

and the length was 2x, so we multiply the result for the with by 2:

`\text{length}\longrightarrow2x=2(60)=120\longrightarrow120yd`

And these are the values for the width and the length.

Answer:

The width is 60yd

The length is 120yd