Question

You have 480 feet of fencing to enclose a rectangular garden. You want the length of the garden to be 30 feet greater than the width. Find the length and width of the garden if you use all the fencing

Answer 1

L=135 W=105

Explanation:

Your rectangle has two length sides and two width sides. That means two sides are 30 feet longer than the other sides. If you subtract 60 from 480, you get 420. Divide 420 by 4 and you get 105. So now you know the width sides are 105 feet long, so 105+105=210. Now all you have to do is add 30 to 105 and get 135. That is the length of the two longer sides. So add 135 and 135 to get 270. All you have to do is add 210 and 270 and you end up with the 480 feet of fence you were given. I know this is probably not the fancy way of doing it, but it works.

Answer 2

The length and width of the garden are 135 feet and 105 feet.

SOLUTION:

Given, You have 480 feet of fencing to enclose a rectangular garden.

You want the length of the garden to be 30 feet greater than the width.

Let, the length of the garden be x and width of the be y.

Then, x = y + 30 --- eqn 1

We need to find the length and width of the garden if you use all the fencing.

As we are using the total fencing, the perimeter of the garden area will be 480 feet.

Perimeter of garden = 480

We know that perimeter = 2(length + breadth)

2x + 2y = 480

2(x + y) = 480

x + y = 240 --- eqn (2)

Now, substitute (1) in (2)

(y + 30) + y = 240

2y + 30 = 240

2y = 240 – 30

2y = 210

y = 105

Now substitute y value in (1)

x = 105 + 30

x = 135

Hence, the length and width of the garden are 135 feet and 105 feet.