The Robertson family put a rectangular pool in their backyard with a stone walkway around it. The...

Question:

The Robertson family put a rectangular pool in their backyard with a stone walkway around it. The total length of the pool and walkway is 3 times the total width. The walkway is 2 ft wide.

a. Write an expression for the area of the pool.

b. Find the area of the pool when the total width is 10 ft.

c. Find the area of the pool when the total width is 9 ft.

Rectangle:

A rectangle is a 2-dimensional figure, which has 4 sides. The pair of opposite sides of a rectangle are parallel to each other and are of the same length. The area of a rectangle with length l and width w is {eq}l{\times}w {/eq}

Let the total width be x feet.

Then the total length is 3x feet.

As the walkway is 2 ft wide.

Let the width of the rectangular pool be x-4 feet.

Then the length of the rectangular pool is 3x-4 feet.

a) The expression for area of the rectangular pool will be

\begin{align} A=l{\times}w \\ A=(3x-4){\times}(x-4) \\ A=3x^2-12x-4x+16 \\ A=3x^2-16x+16 \end{align}

b) When the total width is 10 feet.

The area of the rectangular pool will be

\begin{align} A=3x^2-16x+16 \\ A=3(10)^2-16(10)+16 \\ A=3(100)-160+16 \\ A=300-160+16 \\ A=156 \mbox{ square feet} \end{align}

c) When the total width is 9 feet.

The area of the rectangular pool will be

\begin{align} A=3x^2-16x+16 \\ A=3(9)^2-16(9)+16 \\ A=3(81)-144+16 \\ A=243-144+16 \\ A=115 \mbox{ square feet} \end{align}

Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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