Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the height of a triangle is decreased by 40\% and its base is increased by 40\%, what will be the effect on its area?
(a)No change
(b)8\% decrease
(c)16\% increase
(d)16 \% decrease
Answer
Answer (as printed):
Explanation
Let initial base $=b \mathrm{cm}$ and initial height $=h \mathrm{cm}$. Then, initial area $=\left(\frac{1}{2} b h\right) \mathrm{cm}^{2}$. New base $=(140 \%$ of $b) \mathrm{cm}=\left(\frac{140 b}{100}\right) \mathrm{cm}=\left(\frac{7 b}{5}\right) \mathrm{cm}$. New height $=(60 \%$ of $h) \mathrm{cm}=\left(\frac{60 h}{100}\right) \mathrm{cm}=\left(\frac{3 h}{5}\right) \mathrm{cm}$. $$\text { New area }=\left(\frac{1}{2} \times \frac{7 b}{5} \times \frac{3 h}{5}\right) \mathrm{cm}^{2}=\left(\frac{21}{50} b h\right) \mathrm{cm}^{2} .$$ Area decreased $=\left(\frac{1}{2} b h-\frac{21}{50} b h\right) \mathrm{cm}^{2}=\left(\frac{4}{50} b h\right) \mathrm{cm}^{2}$. Percentage decrease $=\left(\frac{4 b h}{50} \times \frac{2}{b h} \times 100\right) \%=16 \%$.