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प्रश्न
The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas.
उत्तर
Let the two triangles be ABC and DEF with altitudes AP and DQ, respectively.
It is given that Δ ABC ~ Δ DEF.
We know that the ration of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.
`(ar(ΔABC))/(ar(ΔDEF))=(AP)^2/(DQ)^2`
⇒ `(ar(ΔABC))/(ar(ΔDEF))=6^2/9^2`
=`36/81`
=`4/9`
Hence, the ratio of their areas is 4 : 9
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