Question

18. The length and the breadth of a rectangle are in the
ratio 2:1. If the length is increased by 10% and the
breadth is decreased by 50% then, the perimeter of
the new rectangle is 54 units. Find the dimensions
of the original rectangle.​

Answer 1

length =10 CM

breadth =5CM

let the ratio of length and breadth of original rectangle = 2x and x

perimeter of rectangle = 2 (l+b)

=2(2x+x)

=2×3x

=6x

when the length is increased by 2cm and breadth by 3cm then

the length=2x+2

the breadth=x+3

the perimeter of the rectangle =2(l+b)

=2{(2x+2) + (x+3)

=2 (3x+5)

=6x+10

the ratio of the new rectangle and the original rectangle = the perimeter of new rectangle /the perimeter of original rectangle

4/3 = 6x+10 / 6x

24x=18x + 30

24x - 18x=30

6x=30

x=30÷6

x=5

length of the original rectangle =2x

=2×5

=10cm

breadth of the original rectangle =x

=x × 5

=5cm