Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 350: 42

Answer

Area is decreased by 16%.

Work Step by Step

Lets take the initial base of a rectangle be b and the height be h Base is increased by 20% of b therefore final Base = 1.2 b The altitude is decreased by 30 % of h Final altitude =0.7 h The area of rectangle whose base has length b and altitude has length h is given by A = bh Initial area of rectangle = bh Final area of rectangle = (1.2b) * (0.7h) = 0.84bh Increase in area of rectangle in percentage = $\frac{final area - initial area}{initial area}$ * 100 =$\frac{0.84bh - bh}{bh}$ * 100 =$\frac{-0.16bh}{bh}$ * 100 = -0.16 * 100 = -16% therefore 16% area is decreased
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