You are trying to find the area of a deck that is surrounding a rectangular pool. The length of the deck is 2x + 1 and the width

Question

3 years ago

13

is 5x + 2. The pool is a square with sides of 2x. Write a Polynomial that represents the area of ONLY the deck

1 answer:

OverLord2011 [107] · Answer 1 · 2022-05-05T18:08:05+03:00

Answer:

6x² + 9x + 2

Step-by-step explanation:

The pool is a square with a side length of 2x.

The area of the pool = length * length = 2x * 2x = 4x²

The area of the deck surrounding the pool has length of 2x + 1 and width of 5x + 2. Therefore:

The area of the deck surrounding the pool = length * width = (2x + 1)(5x + 2) = 10x² + 4x + 5x + 2 = 10x² + 9x + 2

Area of the deck only = area of the deck surrounding the pool - area of pool = (10x² + 9x + 2) - 4x²

Area of the deck only = 6x² + 9x + 2