Question

Here is a rectangle ABCD.

The length of the rectangle is increased by 10%.
The width of the rectangle is increased by 5%.
Find the percentage increase in the perimeter of the rectangle.

Answer 1

-The length of the rectangle is increased by 10%.

= 30 x 10%

= 3 + 30

= 33

-The width of the rectangle is increased by 5%.

= 20 x 5%

= 1 + 20

= 21

Find the percentage increase in the perimeter of the rectangle.

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.

(33 + 21 ) x 2

= 54 x 2

= 108

other ways

( 33+33 ) + ( 21 + 21)

= 66 +42

=108

Answer 2

8% increase

Explanation:

the perimeter (P) is the sum of the 4 sides

P of rectangle = (2 × 30) + (2 × 20) = 60 + 40 = 100 cm ← original rectangle

An increase of 10% on length = 100 + 10 = 110%

new length = 110% × 30 cm =
`(110)/(100)` × 30 = 1.1 × 30 = 33 cm

An increase of 5% on width = 100 + 5 = 105%

new width =
`(105)/(100)` × 20 = 1.05 × 20 = 21 cm

P of new rectangle

= (2 × 33) + (2 × 21)

= 66 + 42 = 108 cm

since the original P is 100 cm and new P is 108 cm

then there is a percentage increase of 108 - 100 = 8%