## 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 is 5x + 2.

Question

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

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3 weeks 2021-09-01T17:52:57+00:00 1 Answers 0 views 0

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