Given that ΔABC ΔPQR. (i) If ar(ΔABC) = 49 cm2 and ar(ΔPQR) = 25 cm2 and AB = 5.6 cm, find the length of PQ. (ii) If ar(ΔABC) = 28 cm2 and ar(ΔPQR) = 63 cm2 and PR = 8.4 cm, find the length of AC. (iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm2 determine ar(ΔPQR).

Question

KnowledgeBoat · Accepted Answer

(i) Given, ΔABC ΔPQR ar(ΔABC) = 49 cm2 ar(ΔPQR) = 25 cm2 AB = 5.6 cm We know that, The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Hence, PQ = 4 cm. (ii) Given, ΔABC ΔPQR ar(ΔABC) = 28 cm2 ar(ΔPQR) = 63 cm2 PR = 8.4 cm We know that, The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Hence, AC = 5.6 cm. (iii) Given, ΔABC ΔPQR BC = 4 cm QR = 5 cm ar(ΔABC) = 32 cm2 We know that, The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Hence, ar(ΔPQR) = 50 cm2.

Mathematics

Given that ΔABC ∼ ΔPQR.
(i) If ar(ΔABC) = 49 cm² and ar(ΔPQR) = 25 cm² and AB = 5.6 cm, find the length of PQ.
(ii) If ar(ΔABC) = 28 cm² and ar(ΔPQR) = 63 cm² and PR = 8.4 cm, find the length of AC.
(iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm² determine ar(ΔPQR).

Similarity

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