Question

The perimeter of a fence is 140 feet. The sum of three times the length and two times the width is 180 feet. What are the length and width of the fence?

Answer 1

The length of the fence is
`40\ ft`

The width of the fence is
`30\ ft`

Explanation:

Let

x-----> the length of the fence

y----> the width of the fence

we know that

The perimeter of the fence is equal to

`P=2(x+y)`

`P=140\ ft`

so

`140=2(x+y)`

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

`3x+2y=180` -----> equation B

Using a graphing tool----> solve the system of equations

Remember that the intersection point both graphs is the solution of the system of equations

The solution is the point
`(40,30)`

see the attached figure

therefore

The length of the fence is
`40\ ft`

The width of the fence is
`30\ ft`