Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.10 - Modeling with Functions - Concept and Vocabulary Check - Page 291: 4


The area, A of the rectangle $A=xy$. The perimeter, P of rectangle is $P=2x+2y$. If the perimeter of the rectangle is $180\ \text{inches}$, then $y=90-x$. Substituting this formula for y in the expression of area, the area of a rectangle can be expressed as $A\left( x \right)=x\left( 90-x \right)$.

Work Step by Step

Consider the length and breadth of the rectangle Length is x, breadth is y. $\begin{align} & \text{Area of rectangle}=L\cdot B \\ & \text{Perimeter of rectangle}=2\left( L+B \right) \end{align}$ Where L, B are the length and breadth of the rectangle. Now, $\begin{align} & \text{Area of rectangle}=L\cdot B \\ & =x\cdot y \\ & =xy \end{align}$ And $\begin{align} & \text{Perimeter of rectangle}=2\left( L+B \right) \\ & =2\left( x+y \right) \\ & =2x+2y \end{align}$ Now, the perimeter of the rectangle is $180\ \text{inches}$. From here, $2x+2y=180$ Divide both sides by 2 $\left( x+y \right)=90$ From here, $y=90-x$ Now, the area of the rectangle is given by: $\begin{align} & \text{Area of rectangle}=x\cdot y \\ & =x\left( 90-x \right) \end{align}$
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