Change in the Area

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

  1. nycmathguy

    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

    Note: The answer is D. Why is the answer 0%?
    Can you draw a rectangle to visually explain what's going on here?
     
    nycmathguy, Jul 31, 2022
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  2. nycmathguy

    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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    nycmathguy likes this.
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  3. nycmathguy

    nycmathguy

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    Thank you very much. I'm glad to know you.
     
    nycmathguy, Aug 1, 2022
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