Question

The O'Brien's are building a rectangular deck around the outside of their circular pool.

a.) Find the combined area of the deck and the pool if the deck is (2x + 3) units wide by (5x + 6) units long. (A =LW) Show all work.

b.)If the area of the pool is 3x^2 + 7x + 6, what is the area of just the deck?

Answer 1

A:

Width of the deck =
`2x+3` units

Length of the deck =
`5x+6` units

So area of rectangular deck = Length * width

=
`(5x+6)(2x+3)`

Area =
`10x^(2)+15x+12x+18`

Area=
`10x^(2)+27x+18` units square

As mentioned in part B, the area of the pool is
`3x^(2)+7x+6` so the combined area of the deck and pool is

Area = area of rectangular deck + area of pool

=
`13x^(2)+34x+24` unit square

B:

The area of only the deck is
`10x^(2)+27x+18` unit square