A rectangular vegetable garden has a area of 66 square feet. The length of the garden is 1 foot less than twice the width. Find the dimensions of the vegetable garden.

Answer 1

Hello, Sabrina,

This was harder than I first thought. We have two unknowns, so find at least two equations that will allow us to eventually substitute one unknown for the other.

We know that area, A, is 66 ft²

Area is the product of length (L) times width W) of a rectangle.

66 ft² = L*W

We are told that length is one foot less than twice the width:

L = 2W - 1

Let's substitute this definition of length in the first equation:

66 ft² = (2W-1)*W

66 ft² = 2W² - W

Rewrite it as:

0 = 2W² - W - 66

I had to multiply by -1 and move it around to get it into a form my mind needed to find the factors

-2W² + W + 66 = 0

We need to find the factors of this equation. Ouch. This is where I hesitated, but I eventually found the following solution after multiplying it by a -1:

2W² - W - 66 = 0

(W - 6)(2W + 11) = 0

Thus, W can have two solutions of 6 and -11/2. Both are in units of feet. The choice of -11/2 feet as a real solution was a little too Star Wars for me, but for a Klingon in another dimension, it would work.

If we select the 6 foot solution, the vegetable garden works for us humans. Try it:

W = 6 ft

If L = 2W - 1, then L would be 11 ft

Area = 6 ft * 11 ft = 66 ft²

So it works.

I hope this helps,

Bob