AABC - APQR such that ar( AABC) = 36cm² and ar( APQR) = 49cm². If AB = 6cm, then,
PQ = 10cm.
Reason(R): The ratio of the areas of two similar triangle are equal to the ratio of squares of any two corresponding sides.
(a) Both Assertion (A) and Reason (R) are correct and Reason is the correct explanation of Assertion.
(b) Both Assertion (A) and Reason(R) are correct but Reason is not the correct explanation of Assertion.
(c) Assertion is correct but Reason is incorrect.
(d) Assertion is incorrect but Reason is correct.
Answers
Solution :-
given that,
→ ∆ABC ~ ∆PQR
So,
→ ar( AABC) / ar( APQR) = (AB)² / (PQ)² { when two ∆'s are similar, ratio of their areas = Square of their corresponding sides.. }
given that,
→ ar( AABC) = 36cm²
→ ar( APQR) = 49cm².
→ AB = 6 cm .
then,
→ 36/49 = 6²/PQ²
→ (6)²/(7)² = 6²/PQ²
→ (6/7)² = (6/PQ)²
→ (6/7) = (6/PQ)
→ PQ = 7 cm .
therefore,
→ Assertion (A) :- PQ = 10cm.
- False .
- As PQ = 7 cm .
→ Reason(R) : The ratio of the areas of two similar triangle are equal to the ratio of squares of any two corresponding sides.
- True .
Hence, Option (d) Assertion is incorrect but Reason is correct .
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