Chapter 8.1, Problem 42E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# If the length of the base of a rectangle is increased by 20 percent but the length of the altitude is decreased by 30 percent, by what percentage is the area changed? Is this an increase or a decrease in area?

To determine

The percentage of the area which is increased or decreased,

Explanation

Converting theoretical statement into mathematical statement and the calculation is followed by suitable geometric formulae.

Calculation:

Given,

Percentage of base increased of rectangle =20

Percentage of height decreased of the rectangle =30

Let b and h are the base and altitude of the rectangle.

Increased length of the base =b+20100(b)

=b+(0.2)b

=(1+0.2)b

base=1.2b

Increased length of the height =hâˆ’30100(h)

=hâˆ’0.3h

=(1âˆ’0.3)h

=(0.7)h

Height =0

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