Question

PLEASE HELP ME LOL

A gardener wants to create a rectangular vegetable garden in a backyard. He wants it to have a total area of 112 square feet, and it should be 14 feet longer than it is wide. What dimensions should he use for the vegetable garden? Round to the nearest hundredth of a foot.

12.69 feet by 26.69 feet

10.58 feet by 24.58 feet

5.69 feet by 19.69 feet

3.58 feet by 17.58 feet

Thank you so much!

:)

Answer 1

If the gardener want the length to be 14 feet longer than it is wide, then L=w+14. We are given an area of 112. The area formula for a rectangle is A=L*W. Filling in accordingly, 112 = (w+14)(w). Distributing we have
`112=w^2+14w`. We are looking for the dimensions of the garden, so we have to solve for w. To do that we have to factor. Set it equal to 0 to get the quadratic
`w^2+14w-112=0`. Plug that into the quadratic formula to get w values of 5.69 and -19.69. The 2 things in math that will never EVER be negative are time and distance/length so we will not use the negative value. Therefore, our width is 5.69. Our length of w+14 is then 5.69+14 is 19.69. There's our dimensions: width is 5.69 and length is 19.69