If the length of a rectangle is increased
by 40%, and the breath is decreased by
20%, then the area of the rectangle

Question

If the length of a rectangle is increased
by 40%, and the breath is decreased by
20%, then the area of the rectangle
increases by x%. Then the value of x is​

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Cora 2 years 2021-06-22T03:00:53+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-06-22T03:02:10+00:00

    Step-by-step explanation:

    Let the initial length be L.

    And, the initial breadth be B.

    Therefore, Initial Area = L × B

    Now, Final length = L+ \frac{40}{100} L

    = 0.4 L

    And, Final breadth = B – \frac{30}{100} B

    = 0.7 B

    Thus, Final Area = 0.98 LB

    As we can see, there is a decrease in the area.

    So, Decrease in Area = LB – 0.98 LB

    ∴ % decrease in area = \frac{0.02 LB}{LB} × 100

    = 2%

    Or Simply:

    Let the length of rectangle = 100 m

    And, Let the breadth of rectangle = 10 m

    Now, It’s area = 1000 m²

    Reduce the length by 30% to make it 70 m.

    Increase the breadth by 40% to make it 14 m.

    So, The altered area = 980 m²

    Thus, The net reduction in Area = \frac{1000 – 980}{1000} × 100

    = \frac{20}{1000} × 100 = 2 %

    ∴ By reducing the length of the rectangle by 30% and increasing the breadth by 40%, the area reduces by 2%.

    There’s another small method:

    Change in area is given by,

    So, A + B + \frac{AB}{100}

    ⇒ 40 + (-30) + \frac{40 x -30}{100}

    ⇒ 40 – 30 – 12

    = – 2 %

    Or, Area is reduced by 2%.

    This method uses the direct relation, that’s why it’s a bit small. I recommend uh to not use in the exams as they will not entertain any method out of the textbook. The first 2 methods are perfect for exams though.

    Hope This Helps 🙂

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