If a rectangular parking lot has a length that is 3 yards greater than its width and the area is 700 square feet, what is the length and width?

Question

Algebra. 

Length?

Width?

 

Answer 1

Here's what we know:

A = l * w

A = 700

l = w + 3

 

Let's put our values into the equation:

700 = w(w + 3)

700 = w² + 3w

0 = w² + 3w - 700

 

As you can see, what we have here is a quadratic equation just waiting to be factored out.

the 3w is close to 0 compared to the 700, so our factored numbers are going to be pretty close to each other. √700 is a bit more than 26, so let's try dividing by 25:

700 / 25 = 28

28 - 25 = 3

0 = (w + 28)(w - 25)

w = -28, 25

We cannot have a negative length for a side, so the width is 25 feet.

 

l = 25 + 3 = 28

The length is 28 feet long.