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Question
If ∆ABC and ∆DEF are two triangles such that\[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\], then write Area (∆ABC) : Area (∆DEF)
Solution
GIVEN: ΔABC and ΔDEF are two triangles such that .
TO FIND: Area (ABC) : Area (DEF)
We know that two triangles are similar if their corresponding sides are proportional.
Here, ΔABC and ΔDEF are similar triangles because their corresponding sides are given proportional, i.e. \[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\]
Since the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides.
`⇒ (Area(Δ ABC))/(Area(Δ DEF))=9/12`
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