Question

The floor of a rectangular deck has a length that is 6 feet more than it’s width, x. Hakeem is building the deck and decided to increase both dimensions by 3 feet. What is the new area, D, of the floor of the deck?

A. x^2 + 12x + 27
B. x^2 + 9x + 18
C. x^2 + 9x
D. x^2 +6x

Answer 1

Let the width of the rectangular deck be = x feet

The length is 6 feet more than the width so length is = x+6 feet

Let us assume that a total 3 feet is increased (1.5 feet on both ends)

As Hakeem decided to increase both dimensions by 3 feet, this means 1.5 feet is increased on both sides of the deck. So, length and width increases by 3 feet each.

Hence, new length is = x+6+3 = x+9 feet

New width is = x+3 feet

So new area = length*width

D =
`(x+9)(x+3)`

=
`x^(2)+3x+9x+27`

=
`x^(2)+12x+27` square feet

Hence, option A is correct.