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. $$ax : by$$
B. $$\frac{a}{x}$$ : $$\frac{b}{y}$$
C. $$ay : bx$$
D. $$\frac{x}{a}$$ : $$\frac{b}{y}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \frac{a}{b} = \frac{{\frac{1}{2}x \times {h_1}}}{{\frac{1}{2}y \times {h_2}}}bx{h_1} = ay{h_2} \cr & \Leftrightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{{ay}}{{bx}} \cr} $$\[\left[ \begin{gathered} {\text{Ratio of areas}} = \frac{a}{b}{\text{ }} \hfill \\ {\text{Ratio of base}} = x:y \hfill \\ \end{gathered} \right]\]
$${\text{Hence, }}{h_1}:{h_2} = ay:bx$$
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The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
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