Q12 of 56 Page 6

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Given: AD = 6 cm


PS = 9 cm


To find: The ratio of areas


Theorem Used:


1) The ratio of the areas of two similar triangles are equal to the ratio of the squares of their heights.


2) If two triangles are similar, then the ratio of their corresponding sides are equal.


Explanation:



We have,


ΔABC ~ ΔPQR


AD = 6cm


PS = 9cm


By area of similar triangle theorem


…… (i)


In ΔABD and ΔPQS


∠B = ∠Q (ΔABC ~ ΔPQS)


∠ADB = ∠PSQ (Each 90°)


Then, ΔABD ~ ΔPQS (By AA Similarity)


So, (Corresponding parts of similar Δ are proportional)


Or,


Or, …. (ii)


Compare equation (i) and (ii)



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