Question

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

Answer 1

Answer:

The length of the rectangle is 6 meters

Step-by-step explanation:

Let the width of the rectangle is x meters

since the length of a rectangle is the sum of the width and 2, then the length is (x + 2) meters

Area of the rectangle is the product of the length and width of the rectangle, since the Area is 48 units from the question

Area = L * W

48 = (x + 2) * x

48 =  x ( x + 2)

48 = x² + 2x

x² + 2x - 48 = 0

using factorization method, we have

x² + 8x - 6x - 48 = 0

x ( x + 8) -6 ( x + 8) = 0

(x - 6) (x + 8) = 0

The product of any factor is Zero, then at least one of them must be Zero. Algebraically, if a.b = 0, then a = 0 or b = 0

x - 6 = 0

x = 4   or

x + 8 = 0

x = -8

Since the lengths are positive, then only the positive value in the above solutions, so width is 4 meters and the length is 4 +2 = 6 meters.