Question

The length of a rectangle is halved, while its breadth is tripled. what is the percentage change in area? a. 25% increase b. 50% increase c. 50% decrease d. 75% decrease

Answer 1

Let the length be x and breadth be y

original area = length × breadth

= xy

If length is halved and breadth is tripled so they became x/2 & 3y

changed area = x/2 ×3y

= 3xy/2

change in area = 3xy/2 - xy

= 3xy - 2xy /2

=xy/2

In percentage = xy/2 ÷ xy × 100

=xy/2 ×1/xy ×100

= 100/2

= 50

so area change in 50 %

Answer 2

old length be l

old breadth be b

new length is l/2

new breadth is 3b

area of the rectangle a=l×b

therefore l/2×3b= 3lb/2

new area = 3lb/2 - lb

= lb/2

percentage = lb/2×1/lb×100

= 50% increase