The length of a rectangle is 2 units more than the width. The area of the rectangle is 48 units. What is the length, in units, of the rectangle?

Answer 1

The area (A) of a rectangle is calculated by multiplying the length (l) by the width (w).

If we use the variable w to represent the width of the rectangle, then we can write:

A = l • w

In this problem, the length is equal to two more than the width or w + 2

Then A = (w + 2) • w

We can solve for w using the area of 48:

A = (w + 2) • w

A = w ² + 2w

48 = w ² + 2w

48 - 48 = w ² + 2w - 48

0 = w² + 2w - 48

This equation can be factored as 0 = (w + 8) (w-6)

There are two solutions for this equation: w = -8 and w = 6

Since the width can not be a negative number, we will select w = 6

Then the length will be w + 2 = 6 + 2 =8

The width will be 6 units.

The length will be the width + 2 = 8 units.