## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Test - Page 879: 17

#### Answer

The dimensions of the rectangular plot are $x=12\text{ feet, }y=15\text{ feet}$ or $x=\frac{15}{2}\text{ feet, }y=24\text{ feet}$.

#### Work Step by Step

The length of the plot is y and the width is x. Hence, the perimeter of three sides is the sum of all the sides of the rectangular plot which is as shown below: $2x+y$ and it is given as $39$ feet, that is, $2x+y=39$ (I) So, the area of the rectangular plot is 180 square feet, which is, $length\times breadth$ $xy=180$ (II) From equation (II), obtain the value of y: $y=\frac{180}{x}$ Put the value of y in equation (I) to obtain the value of x: $2x+\frac{180}{x}=39$ Simplify $2{{x}^{2}}-39x+180=0$ Factorize the equation and solve as shown below: \begin{align} & 2{{x}^{2}}-24x-15x+180=0 \\ & 2x\left( x-12 \right)-15\left( x-12 \right)=0 \\ & \left( x-12 \right)\left( 2x-15 \right)=0 \end{align} Equate each factor to 0, which gives $\left( x-12 \right)=0$ or $\left( 2x-15 \right)=0$ Therefore, $x=12$ or $x=\frac{15}{2}$ Put $x=12$ in equation (II); this gives $y=15$ Substitute $x=\frac{15}{2}$ in equation (II); this gives $y=24$ Therefore, the dimensions of the rectangular plot are either $x=12\text{ feet, }y=15\text{ feet}$ or $x=\frac{15}{2}\text{ feet, }y=24\text{ feet}$.

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