The areas of two similar triangles are $25 c m^{2}$ and $36 c m^{2}$ respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.

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Solution

From the property of similar triangles:
Ratio of area of similar triangles = (Ratio of Corresponding sides)
$25 over 36 equals left parenthesis fraction numerator A l t i t u d e space o f space f i r s t space t r i a n g l e over denominator A l t i t u d e space o f space s e c o n d space t r i a n g l e end fraction right parenthesis squared 5 over 6 equals fraction numerator 2.4 over denominator x end fraction x space equals fraction numerator 14.4 over denominator 5 end fraction equals 2.88 space c m$
The corresponding altitude is 2.88 cm.

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