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The length of a rectangular swimming pool is 2x-1 meters and the width is x+2 meters. (a) Write...

Question:

The length of a rectangular swimming pool is {eq}2x-1 {/eq} meters and the width is {eq}x+2 {/eq} meters. (a) Write a polynomial {eq}A(x) {/eq} that represents the area. (b) Find {eq}A(5) {/eq}.

Rectangle

A rectangle is a two dimensional figure with two pair of equal straight sides that are all at right angles, i,e. {eq}90^o. {/eq}

The image shown below is a figure of rectangle ABCD

Following are the properties of a rectangle:

Area: length * width

Perimeter: 2* (length + width)

Number of Sides: 4

Number of edges: 4

Sum of angles : 360

Answer and Explanation:

The dimension of rectangular swimming pool is {eq}(2x-1) \times (x+2) {/eq}

Part a.) Area of the rectangular pool is:

$$Area =length \times width $$

$$A(x) =(2x-1)*(x+2) $$

$$A(x) =2x^2+4x- x-2 $$

$$A(x) =2x^2+3x-2 $$

Part b.) Area at {eq}x=5 {/eq}

$$A(x) =2x^2+3x-2 $$

$$A(5) =2(5)^2+3*5-2 $$

$$A(5) =2*25+15-2 $$

$$A(5) =50+13 $$

$$A(5) =63\ m^2 $$

Area of the rectangular swimming pool at {eq}A(5) {/eq} is {eq}63\ m^2. {/eq}


Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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