Question

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?

Answer 1

Answer:

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