Change in the Area

[nycmathguy]

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

Note: The answer is D. Why is the answer 0%?
Can you draw a rectangle to visually explain what's going on here?

 

[MathLover1]

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%

 

[nycmathguy]

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%

Thank you very much. I'm glad to know you.