Question

If the base of a parallelogram decreases by $20$%, and the height increases by, $40$% by what percent does the area increase?

Answer 1

• Let the height of parallelogram is $h$ and the base of parallelogram is $b$
• Area of parallelogram is $\frac{hb}{2}$
• Base is reduced by $20$% , New length of base is $b(1-\frac{1}{5})=\frac{4b}{5}$
• Height is increased by $40$%, New length of height is $h(1+\frac{2}{5})=\frac{7h}{5}$
• The area of parallelogram is $\frac{1}{2}\times \frac{4b}{5}\times \frac{7h}{5}=\frac{14bh}{25}$
• Percentage Increase in area is $(\frac{14bh}{25}-\frac{bh}{2})/\left(\frac{bh}{2}\right)\times 100=\frac{(28-25)}{25}\times 100=\frac{3}{25}\times 100=12$%