Question

If the lengths of a rectangle is decreased by 40% and the breadth is increased by 30%, then find the percentage change in the area of the rectangle. (A) 28% (B)-35% (C)-- 22% (D) -40%

Answer 1

Answer:

buy-----------------------------------------------

Answer 2

Answer:

Option C

Step-by-step explanation:

Given :-

The length of a rectangle is decreased by 40% and the breadth is increased by 30%.

To find :-

Find the percentage change in the area of the rectangle. ?

(A) 28% (B)-35% (C)-- 22% (D) -40%

Solution :-

Let the length of a rectangle be l units

Let the breadth of a rectangle be b units

Area of a rectangle = lb sq.units

If the length of a rectangle is decreased by 40% then the new measure of the length

=> l - 40% of l

=> l -(40%×l)

=> l -(40/100)×l

=> l -(2/5)×l

=> l -(2l/5)

=> (5l-2l)/5

=> 3 l/5 units

If the breadth of a rectangle is increased by 30% then the new measure of the breadth

=> b + (30% of b)

=> b +(30% ×b)

=> b +(30/100)×b

=> b +(3/10)×b

=> b +(3b/10)

=> (10b+3b)/10

=> 13b/10 units

Now,

Area of the new Rectangle

=> (3 l/5)×(13b/10)

=> (3l×13b)/(5×10)

=> 39lb/50 sq.units

Original area = lb sq.unitd

New area = 39lb/50 sq.units

Original Area > New Area

=> Decreasing in the area

=> Original area - New area

=> lb - (39lb/50)

=> (50lb-39lb)/50

=> 11lb/50 sq.units

Now,

The percentage decreased in the area

=> (Decreasing in the Area / Original Area ) ×100

=> [(11lb/50)/(lb)]×100

=> (11lb/50lb)×100

=> (11/50)×100

=> 11×2

=> 22 %

Decreasing Percentage in the area = 22 %

Symbolically it is -22%

Answer:-

The percentage change in the area of the rectangle is -22%

Used formulae:-

→ Area of a rectangle = lb sq.units

• l = length
• b = breadth