A farmer has 70 meters of fencing to use to create a rectangular garden in the middle of an open field.

Question

I keep getting the width is 30 but keeps saying it is wrong so i am stuck, thank you for the help!

A farmer has 70 meters of fencing to use to create a rectangular garden in the middle of an open field.

Let  represent the length of the rectangular garden (in meters).

Suppose the length of the garden is 10 meters ().

What is the width of the garden?

What is the area of the garden?

Write an expression in terms of hat represents the width of the garden (in meters).

Write an expression in terms of  that represents the area of the garden (in meters).

Answer 1

Building a fence around a rectangular field indicates that we are using the perimeter. The perimeter of a rectangle is found by adding up all the sides, which is two lengths and two widths.

P = W + W + L + L

or we can write it like this

P = 2W + 2L

In this problem, the total amount of fence is 70m. So P = 70. And we are told that the length of the garden is L=10m. Now we can substitute these into the equation.

70m = 2W + 2(10m)

70m = 2W + 20m

50m = 2W

25m = W

So you were really close!

Now you can find the area of the garden by the equation of area of a rectangle:

A = L × W

And you can rearrange and sub values in to the perimeter and area equations to find the answers to the final questions.