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​

Answer 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 :)