Question

The width of a rectangle is 3 units less than the length. The area of the rectangle is 54 units. What is the length,in units of the rectangle?

Answer 1

9 units

Explanation:

length: L

Width: L - 3

Area = length × width

(L - 3) × L = 54

L² - 3L - 54 = 0

L² - 9L + 6L - 54 = 0

L(L - 9) + 6(L - 9) = 0

(L - 9)(L + 6) = 0

L = 9, -6

L = 9

Answer 2

The length is 9 units

Explanation:

Let x = length

width = x-3

Area = 54 = l*w

54 = x * (x-3)

Distribute

54 = x^2 -3x

Subtract 54 from each side

54-54 = x^2 -3x-54

0 = x^2 -3x-54

Factor

What 2 number multiply to -54 and add to -3

-9 * 6 =54

-9+6 =-3

(x-9) (x+6) =0

Using the zero product property

x=9 x=-6

Since we cannot have negative length

x=9 units

The length is 9 units