Discussion
The ratio of altitude of two triangles is 4:5 and the ratio of their areas is 3:2, then the ratio of their corresponding bases is
Answer: D
The ratio of the bases is 15:8.
The area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\), so the ratio of bases is the ratio of areas divided by the ratio of heights.
\[ \begin{aligned} \frac{b_1}{b_2} &= \frac{A_1 / A_2}{h_1 / h_2} \\ &= \frac{3/2}{4/5} = \frac{15}{8} \end{aligned} \]
8:15 inverts the answer, and 7:8 comes from wrongly subtracting or adding the ratio terms instead of dividing.
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