Question

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

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