Question

A rectangular garden has a perimeter of 172 feet. The length of the garden is 24 feet more than the width. What are the dimensions of the garden? (Recall the formula P = 2L + 2W.)

Answer 1

Let the width be x, then length = 24 +x
Perimeter = 2(length + width)
2(x + 24 + x) = 172
2(2x + 24) = 172
4x - 48 = 172
4x = 172 + 48 = 220
x = 220/4 = 55

Therefore, width is 55 and length is 55 + 24 = 79

Answer 2

Perimeter of a rectangle is given by:

`P= 2(L+W)` .....[1]

where

P is the perimeter of a rectangle

L is the length of the rectangle

W is the width of the rectangle.

As per the statement:

A rectangular garden has a perimeter of 172 feet.

⇒P = 172 feet

It is also given that:

The length of the garden is 24 feet more than the width.

⇒
`L= 24+W`

Substitute the given values in [1] we have;

`172=2(24+W+W)`

Combine like terms;

`172=2(24+2W)`

Divide both sides by 2 we have;

`86=24+2W`

Subtract 24 from both sides we have;

`62=2W`

Divide both sides by 2 we get;

31 feet = W

Then;

`L= 24+31 = 55` feet.

therefore, the dimension of the garden are:

`L= 55` feet and W = 31 feet