Question

The length of your family's garden is 3 feet greater than the width. The area of the garden is 460 square feet. What are the dimensions of the garden?

Answer 1

Given:

The length of your family's garden is 3 feet greater than the width.

The area of the garden is 460 square feet.

To find:

The dimensions of the garden.

Solution:

Let x feet be the width of the garden. Then,

Length =
`x+3` feet

The area of a rectangle is:

`A=l* w`

Where, l is the length and w is the width of the rectangle.

The area of the rectangular garden is:

`A=(x+3)* x`

`A=x^2+3x`

It is given that the area of the garden is 460 square feet.

Putting
`A=460`, we get

`460=x^2+3x`

`0=x^2+3x-460`

Splitting the middle term, we get

`x^2+23x-20x-460=0`

`x(x+23)-20(x+23)=0`

`(x+23)(x-20)=0`

`x=-23,20`

The width of a garden cannot be negative. So,
`x=20`.

Now,

`l=x+3`

`l=20+3`

`l=23`

Therefore, the length of the garden is 23 feet and the width of the garden is 20 feet.