ΔABC ∼ ΔEDF and ar(ΔABC) : ar(ΔDEF) = 1 : 4. If AB = 7 cm, BC = 8 cm and CA = 9 cm, then DF is equal to?
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e.16 cm
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Concept |
Understanding |
Application |
Fair calculation |
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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 ~ ΔEDF AB = 7 cm, BC = 8 cm, AC = 9 cm And Area(ΔABC) :Area(ΔEDF) = 1 : 4, |
Hence, Area(ΔABC) : Area(ΔEDF) = (BC/DF)2 ⇒1/4 = (8/DF)2 ⇒ DF2 = 64 × 4/1 ⇒ DF2 = 256 ⇒ DF = 16 |
64 × 4 = 256 |