Question

Farmer fernanda wants to put a fence around her rectangle field . The length of the field is 40 feet less than 3 times the width. If she has 320 feet of fencing, what are the dimensions of the field?

Answer 1

Length: 110 feet

Width: 50 feet

Explanation:

we know that

The perimeter of rectangle is equal to

`P=2(L+W)`

where

L is the length of rectangle

W is the width of rectangle

we have

`P=320\ ft`

so

`320=2(L+W)` ----> equation A

`L=3W-40` ----> equation B

Solve the system by substitution

substitute equation B in equation A

`320=2(3W-40+W)`

solve for W

`320=2(4W-40)`

`320=8W-80`

`8W=320+80`

`8W=400`

`W=50\ ft`

Find the value of L

`L=3(50)-40=110\ ft`

therefore

The dimensions of the field are

Length: 110 feet

Width: 50 feet