ΔABC ∼ ΔPRQ and PQ = 4 cm, QR = 7 cm and PR = 8 cm. If ar(ΔABC) : ar(ΔPQR) = 1 : 4, then AC is equal to:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 2 cm
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Concept |
Understanding |
Application |
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If 2 triangles A and B are similar: Area of triangle A/Area of triangle B = (side of A)2/(side of B)2 |
Given ΔABC ~ ΔPRQ, ⇒ PQ = 4 cm, QR = 7 cm, PR = 8 cm and ar(ΔABC)/ar(ΔPQR) = 1/4 |
⇒ (AC/PQ)2 = ar(ΔABC)/ar(ΔPQR) ⇒ AC2/42 = 1/4 ⇒ AC2 = 16 × 1/4 ⇒ AC = 2 cm |