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how did you solve ques 2??areas of ∆ABC and ∆POR are not equal...only both ∆s are similar.According to Area Ratio Theorem, if the ratio of areas of two similar∆s is equal, only then that ratio is equal tohe square if their corresponding sides.
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how did you solve ques 2??areas of ∆ABC and ∆POR are not equal...only...
SOLUTION :  

Given:

In ΔABC, D and E are the midpoints of AB and AC respectively.

Therefore, DE II BC (By Converse of mid-point theorem)

Also, DE = 1/2BC

In ΔADE and ΔABC

∠ADE = ∠B    (Corresponding angles)

∠DAE = ∠BAC   (common)

ΔADE–ΔABC (By AA Similarity)

We know that the ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.

ar(ΔADE)/ar(ΔABC) = AD^2/AB^2

ar(ΔADE)/ar(ΔABC) = AD^2 / 2AD^2

[AD = 2AB as D is the mid point]

ar(ΔADE)/ar(ΔABC) = 1^2 /2^2

ar(ΔADE)/ar(ΔABC) = 1/4

Hence, the ratio of the areas ΔADE and ΔABC is ar(ΔADE) : ar(ΔABC) = 1 : 4.
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