Thinking Mathematically (6th Edition)

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

Chapter 10 - Geometry - 10.3 Polygons, Perimeter, and Tessellations - Exercise Set 10.3 - Page 637: 40

Answer

The dimensions of a rectangular field are\[120\text{ yd}\]and\[24\text{ yd}\], respectively.

Work Step by Step

The length and width of a rectangular field will be determined by finding the perimeter of the field in the yard. Computation of length and width of the field by the perimeter can be done by using the formula,\[P=2l+2w\]. Length, l is 5 times of the width, w. Compute the length and width as shown below: \[\begin{align} & P=2l+2w \\ & =2\left( l+w \right) \end{align}\] Substitute the values in the above formula as mentioned below: \[\begin{align} & 288\text{ yd}=2\times \left( 5w+w \right) \\ & 288\text{ yd}=12w \\ & w=\frac{288\text{ yd}}{12} \\ & =24\text{ yd} \end{align}\] Compute the length of the field as mentioned below: \[\begin{align} & l=5\times w \\ & =5\times 24\text{ yd} \\ & =120\text{ yd} \end{align}\] Hence, the length and width of a rectangular fields are\[120\text{ yd}\]and\[24\text{ yd}\].
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