The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
40%
42%
44%
46%
Explanation:
Let original length = $x$ metres and original breadth = $y$ metres.
Original area = $(xy)$ m2.
| New length =$ \left(\dfrac{120}{100} x\right) $m=$ \left(\dfrac{6}{5} x\right) $m. |
| New breadth =$ \left(\dfrac{120}{100} y\right) $m=$ \left(\dfrac{6}{5} y\right) $m. |
| New Area =$ \left(\dfrac{6}{5} x \times\dfrac{6}{5} y\right) $m2=$ \left(\dfrac{36}{25} xy\right) $m2. |
The difference between the original area = $xy$ and new-area 36/25 $xy$ is
= (36/25)$x$$y$ - $x$$y$
= $x$$y$(36/25 - 1)
= $x$$y$(11/25) or (11/25)$x$$y$
| $\therefore$ Increase % =$ \left(\dfrac{11}{25} xy \times\dfrac{1}{25} \times 100\right) $%= 44%. |