Joe has a rectangular chicken coop. the length of the coop is 4 feet less than twice the width. the area of the chicken coop is 510 square feet. what is the length of the chicken coop?

Let w and l be the dimensions (width and length, respectively) of the coop.

We know that the length of the coop is 4 feet less than twice the width, which means that

Also, the area is 510, but the area is the product of the dimensions, so we have

Plug the expression for l in the formula for the area:

We can divide the whole expression by 2 and solve it with the quadratic formula:

So, the two solutions are

The negative solution makes no sense (we can't have negative lengths), so the width must be 17.

We conclude that the length is

Let w and l be the dimensions (width and length, respectively) of the coop.

We know that the length of the coop is 4 feet less than twice the width, which means that

Also, the area is 510, but the area is the product of the dimensions, so we have

Plug the expression for l in the formula for the area:

We can divide the whole expression by 2 and solve it with the quadratic formula:

So, the two solutions are

The negative solution makes no sense (we can't have negative lengths), so the width must be 17.

We conclude that the length is