how do you find the length of a rectangle with a width of 75 and area is at most 6250 square feet?

Question

This problem is an inequality that must be solved.

Answer 1

For rectangles and squares, the area is the product of the length and width:

A = L x W

In your problem, the area and the width are known. What remains unknown is the length. There are several ways to proceed. Either solve the equation for L and then plug in your known numbers, or plug-in your knowns and then solve. I prefer the second way.

The area is at most 6250:

Let A = 6250

The width is 75:

W = 75

6250 = L x 75

Almost. Notice that in the original question, the area “is at most 6250 square feet.” This tells us that the units are feet for length and width, and square feet for area. The “at most” part tells us this is an inequality.

6250 ≥ L x 75

The most that the area, LxW can be is 6250

Divide both sides of the equation by 75, and you get

6250/75 ≥ L x 75 / 75

Or just

6250/75 ≥ L

L ≥ 83 1/3 feet

You can check this answer by plugging in 83 1/3 into the area formula with 75 as the width. Then try it with a number that is greater than 83 1/3 and a number that is less than 83 1/3. You will see that any numbers greater than 83 1/3 give you an area greater than 6250.