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Question
In ΔABC ∼ ΔQRP, `(ar(ΔABC))/(ar(ΔPQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR = ______.
Fill in the Blanks
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Solution
In ΔABC ∼ ΔQRP, `(ar(ΔABC))/(ar(ΔPQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR = 10 cm.
Explanation:
For similar triangles the ratio of areas equals the square of the ratio of corresponding sides, so linear ratio = `sqrt(9/4) = 3/2`. With ΔABC ∼ ΔQRP the vertex correspondence gives BC ↔ PR, hence `(BC)/(PR) = 3/2`.
Therefore `PR = 2/3 xx BC`
= `2/3 xx 15`
= 10 cm
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