# Change in the Area

Discussion in 'Algebra' started by nycmathguy, Jul 31, 2022.

1. ### nycmathguy

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If the length of a rectangle is increased by 25% and the width decreased by 20%, what is the change in the area of the rectangle?

A 20% decrease
B 10% decrease
C 5% decrease
D 0%
E 5% increase

Can you draw a rectangle to visually explain what's going on here?

nycmathguy, Jul 31, 2022

2. ### MathLover1

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Since we have given that

If length is increased by 25%
If breadth is decreased by 20%

So, net change in area of rectangle would be

25-20-(25*20)/100
=5-500/100
=5-5
=0%

to illustrate, you can draw a rectangle with the length 8 and the width 4

area=8*4=32

then you draw new rectangle ( if the length increase by 25% and breadth is decreased by 20%) which will have:

the length 8+0.25*8= 10
and the width 4-0.20*4=3.2

area=10*3.2=32

as you can see both areas are same, so net change in area of rectangle is 0%

MathLover1, Aug 1, 2022
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