The length of a rectangle is 5 units more than the width. The area of the rectangle is 36 units. What is the width, in units, of the rectangle?

4

Step-by-step explanation:

Let y be the width of the rectangle

The length of the rectangle is 5 unit more than the width. This is written as:

Length = y + 5

Area = 36

Recall:

Area of rectangle = length x width

36 = (y + 5) x y

36 = y^2 + 5y

Rearrange the expression

y^2 + 5y - 36 = 0

To solve this problem by factorization, multiply the first term (i. e y^2) and last term (i. e - 36) together. This gives - 36y^2

Next, find two factors of - 36y^2 such that when we add them together it will result to the second term (5y). These factors are - 4y and 9y. Now we substitute - 4y and 9y in place of 5y in the equation. This is illustrated below:

y^2 + 5y - 36 = 0

y^2 - 4y + 9y - 36 = 0

We factorize as follows:

y (y - 4) + 9 (y - 4) = 0

(y + 9) (y - 4) = 0

y + 9 = 0 or y - 4 = 0

y = - 9 or y = 4

Since the measurement can not be negative, therefore y (i. e the width) is 4