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.
