Question

If the area of rectangle is increased by 32% and its breadth is increased find by 20% find % increase in length

Answer 1

Let the length be ‘L’ unit & breadth be ‘B’ unit

So, ORIGINAL PERIMETER = (2L + 2B) unit

ORIGINAL AREA = LB sq unit

NEW BREADTH = B + 10%of B = (B + B/10) = (11B/10)

NEW AREA = LB + 32% of LB =( LB + 32LB/100) = (132LB/100) sq unit

So, NEW LENGTH = area ÷ breadth

= 132LB/100 * 10/11B = 12L/10

So, NEW PERIMETER = 2( 12L/10 + 11B/10) = (12L+11B)/5

Increase in perimeter = (12L +11B)/5 - (2L +2B) =(2L+B)/5

PERCENTAGE INCREASE in perimeter =

(Increased perimeter/ original perimeter)*100

=( 2L+B)/5 * (1/(2L+2B) * 100

= 20(2L+B) / (2L+2B)

= (40L + 20B) / (2L+2B) % = answer.....