The length of a rectangle is 4 inches longer than it is wide. If the area is 32 square inches, what are the
dimensions of the rectangle?
The width, or shorter side is
The length, or longer side is inches

To solve for the dimensions of the rectangle, we start by letting the width be inches. Then, the length would be inches. The area of the rectangle can be expressed as:

Expanding this gives:

Using the quadratic formula, we solve for . The width comes out to be 4 inches, and substituting this back, the length is 8 inches.

Now you know that the width is 4 inches and the length is 8 inches!

Did you know that the concept of area dates back to ancient civilizations? The Egyptians used simple formulas for rectangles hundreds of years ago to calculate land area for agriculture. This historical perspective shows how foundational geometric concepts are to engineering and architecture, still applied today!

In practical scenarios, converting measurements can sometimes cause confusion. Always double-check that you’re working with the same units, especially when dealing with properties like area or volume. A common mistake is mixing inches and feet, which can lead to calculation errors. Standardizing units helps in avoiding these pitfalls!