Question

The length of a rectangle is increased by 25% while breadth is diminished by 30% .What is the impact on area?



The answer is 12.5% decrease​

Answer 1

GIVEN :-

• The length of a rectangle is increased by 25% while breadth is diminished by 30%.

TO FIND :-

• Impact on the area.

SOLUTION :-

Let,

• Length of Rectangle = l.

• Breadth of Rectangle = b.

Area of Rectangle = l × b.

According To the Question,

New Length of Rectangle = 25% of l + l.

= 25 × l/100 + l.

= l/4 + l.

= l + 4l/4.

= 5l/4.

New Breadth of Rectangle = b – 30% of b.

= b – 30 × b/100.

= b – 3b/10.

= 7b/10.

Now,

New Area = New Length × New Breadth.

= New Area = 5l/4 × 7b/10.

= New Area = 7lb/8.

We can clearly see that,

It is a Decrease in the area.

Decrease = Old Area – New Area.

= Decrease = lb — 7b/8.

= Decrease = lb/8.

Now, Calculating Decrease Percentage.

Decrease % = Decrease × 100/Area.

= Decrease % = (lb × 100/8)/lb.

= Decrease % = (12.5 lb)/lb.

= Decrease % = 12.5 %

Therefore, Decrease % = 12.5 %.

Answer 2

New Length

= l + 25/100 x l

= 5l/4

New Breadth

= b - 30/100 xb

= 7b/10

Hence, New area

= 5l/4 x 7b/10

= 7lb/8

Clearly there is a decrease in area.

Decrease

= lb - 7lb/8

= lb/8

So, Decrease %

= (lb/8 x i/lb x 100)%

= 25/2%

= 12.5%