   Chapter 8.1, Problem 41E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

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 and the length of the altitude is increased by 30 percent, by what percentage is the area increased?

To determine

The percentage of the area increased.

Explanation

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

Calculation:

Given,

Percentage of base of the rectangle increased =20

Percentage of the height of (altitude of) the rectangle increased =30

Let b be the base of the rectangle and h be the height (altitude) of the rectangle.

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

=b+0.2b

=(1+0.2)b

base=1.2b

Increased length of the height =h+30100h

=h+0.3h

=(1+0.3)h

=1.3h

Area of the rectangle A1=bh

The area of the rectangle after the change

A2=Base×Height

=1

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