QQuestion
The areas of two similar triangles are in the ratio 9 : 64. The ratio of their corresponding altitudes is:
(a) 3 : 8
(b) 2 : 1
(c) 9 : 64
(d) 8 : 3
ICSEClass XMathematicsSimilarity01 Mark2026 Easy
✓Answer
(a) 3 : 8
Explanation:
For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.
\frac{\mathrm{Area}_1}{\mathrm{Area}_2}=\left(\frac{\mathrm{Altitude}_1}{\mathrm{Altitude}_2}\right)^2⇒ \frac{9}{64}=\left(\frac{\mathrm{Altitude}_1}{\mathrm{Altitude}_2}\right)^2
Taking the positive square root:
⇒ \frac{\mathrm{Altitude}_1}{\mathrm{Altitude}_2}=\frac{3}{8}
Therefore, the ratio is 3 : 8.
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