ΔABC ~ ΔEDF and ar(ΔABC) : ar(ΔDEF) = 4 : 9. If AB = 6 cm, BC = 8 cm and AC = 10 cm, then DF Is equal to(in cm):
Show answer & explanation
Correct answer: C
Explanation
Correct answer is option 3 i.e.12 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 = 6 cm, BC = 8 cm, AC = 10 cm And Area(ΔABC) :Area(ΔEDF) = 4/9, |
Hence, Area(ΔABC) : Area(ΔEDF) = (BC/DF)2 ⇒ 4/9 = (8/DF)2 ⇒ DF2 = 64 × 9/4 ⇒ DF2 = 144 ⇒ DF = 12 |
64 × 9/4 = 16 × 9 = 144 |