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 length is 30 inches and width is 24 inches

Explanation:

Area of rectangle is Length * Width

Let length be L and Width be W

Since area given as 720, we can write:

L* W = 720

Moreover, the Width is 6 inches SHORTER than Length, we can write:

W = L - 6

We put this into the 1st equation and solve for L:

`LW=720\\L(L-6) = 720\\L^2-6L=720\\L^2-6L-720=0\\(L-30)(L+24)=0\\L=-24,30`

Length can't be negative, so L = 30

Now, we know W = L - 6, so

W = 30 - 6 = 24

Thus, the length is 30 inches and width is 24 inches