Subject: General Aptitude · Chapter: Area · Exam: 2004 · Marks: · Difficulty:
The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be
(a)$a x: b y$
(b)$\frac{a}{x}: \frac{b}{y}$
(c)$a y: b x$
(d)$\frac{x}{a}: \frac{b}{y}$
Answer
Answer (as printed): C
Explanation
$\frac{a}{b}=\frac{\frac{1}{2} x \times h_{1}}{\frac{1}{2} y \times h_{2}} b x h_{1}=a y h_{2} \Leftrightarrow \frac{h_{1}}{h_{2}}=\frac{a y}{b x}$. $\left[\right.$ Ratio of areas $=\frac{a}{b}$, Ratio of base $\left.=x: y\right]$ Hence, $h_{1}: h_{2}=a y: b x$.
Explanation as extracted from the printed page; notation may be imperfect.