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

June 22, 2021

By Cora

1 thought on “If the length of a rectangle is increased<br />by 40%, and the breath is decreased by<br />20%, then the area of the rectangle<br”

1. 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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