In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.
Correct Answer: Option B
Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then, \(\frac{\frac12\times x\times3h}{\frac12\times y\times4h}=\frac43\Rightarrow\frac xy=\frac{\displaystyle4}{\displaystyle3}\times\frac{\displaystyle4}{\displaystyle3}=\frac{16}9\)
Required ratio = 16 : 9.
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