Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - Chapter Summary, Review, and Test - Review Exercises - Page 681: 35


The cost to enclose the baseboard around the room is\[\$132\].

Work Step by Step

The cost to enclose field with fencing will be determined by finding the perimeter of the field. Then, multiply the perimeter with the given fencing cost. Computation of perimeter of the field can be done by using the formula\[P=2l+2w\]. Length, l is 35 ft. and width, is 15 ft. Compute the perimeter as shown below: \[\begin{align} & P=2l+2w \\ & =\text{2}\times \text{35ft}+\text{2}\times \text{15ft} \\ & =\text{70ft}+\text{30ft} \\ & =\text{100}\ \text{ft} \end{align}\] It is given that the room has 4 doorways having width of 3 ft. each. No baseboard is required across the doorways. Hence, multiply number of doorways by the length of each doorway and then subtract from the total perimeter. The area around which baseboard has to be put can be determined as shown below: \[\begin{align} & \ \text{Total area of the baseboard}=\text{4 doorways}\ \ \times \ \ \text{3ft} \\ & =\text{12}\ \text{ft} \\ & =\text{100}\ \text{ft}-\text{12}\ \text{ft} \\ & =\text{88}\ \text{ft} \end{align}\] For the computation of cost of baseboard around the room, multiply the perimeter \[\text{88 ft}\]by the cost $1.50 per foot. \[\begin{align} & \text{Cost}=\frac{88feet}{1}\times \frac{\$1.50}{feet}\\&=88\times\$1.50\\&=\$132\end{align}\] Hence, the cost to enclose the baseboard around the room is\[\$132\].
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