Question

A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length in feet of the mat. Then find the area in square feet of the mat

Answer 1

Part 1) The length of the mat is
`12\ ft`

Part 2) The area of the mat is
`72\ ft^(2)`

Explanation:

Part 1)

Let

x-----> the length of the math

y----> the width of the math

we know that

The perimeter of a rectangle is equal to

`P=2(x+y)`

we have

`P=36\ ft`

so

`36=2(x+y)`

`18=(x+y)` ------> equation A

`x=2y` ------> equation B

substitute equation B in equation A and solve for y

`18=(2y+y)`

`3y=18`

`y=6\ ft`

Find the value of x

`x=2(6)=12\ ft`

Part 2) we know that

The area of a rectangle is equal to

`A=xy`

we have

`x=12\ ft`

`y=6\ ft`

substitute the values

`A=(12)(6)=72\ ft^(2)`