Question

A rectangular dog bed has an area of 720 square inches. The width of the bed is 6 inches shorter than the length.

Create and solve for an equation, that represents the area of the bed, that can be used to determine the length and width of the bed.

I used L to represent length and L - 6 to represent width, but I wasn't sure how to solve my equation. (maybe my equation is wrong?)

My equation: L(L - 6) = 720

Any help would be appreciated.

Answer 1

The required equation is
`L(L-6)=720` and the length is 30 inches and width is 24 inches.

Explanation:

Given : A rectangular dog bed has an area of 720 square inches. The width of the bed is 6 inches shorter than the length.

To find : Create and solve for an equation, that represents the area of the bed, that can be used to determine the length and width of the bed ?

Solution :

Let the length be 'L' and width be 'W'.

The width of the bed is 6 inches shorter than the length.

i.e.
`W=L-6`

The area of the rectangular dog bed is
`A=L* W`

Substitute the value,

`720=L* (L-6)`

`L^2-6L-720=0`

`L^2-30L+24L-720=0`

`L(L-30)+24(L-30)=0`

`(L-30)(L+24)=0`

`L=30,-24`

Reject L=-24 (as dimensions are not negative)

The length is 30 inches.

The width is 24 inches.

Therefore, the required equation is
`L(L-6)=720` and the length is 30 inches and width is 24 inches.