Question

if the width of a rectangle is reduced by 20% by what percentage should its length be increased to keep its area equal​

Answer 1

Answer:

25%

explanation:

To start with, If length is reduced, the breadth has to be increased , for having the same area. As the area is the product of length & breadth.

Or in other words, if you want to know, by what quantity the breadth has to be reduced? The answer will be a negative quantity.

If we assume length & breadth as L & B

Area = LB unit² …………(1)

Length is reduced by 20%

ie, 20% of L = 20/100 * L

= L/5

So, new Length = L - L/5 = 4L/5

Let breadth of new rectangle so formed is x unit, so that area remains the same

So new area = 0.8L * x = 0.8Lx unit ² ………..(2)

Eq (1) = eq(2)

=> LB = 0.8Lx

=> B = 0.8 x

=> x = B/0.8

So, for having the same area, breadth = B/0.8 = 5B/4 unit

So breadth should be increased by

5B/4 - B = B/4

So % increase in breadth = (B/4) /B * 100

= 25% ………….ANS

hope this helps. please mark brainliest :)