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If ∆Abc and ∆Def Are Two Triangles Such that a B D E = B C E F = C a F D = 3 4 , Then Write Area (∆Abc) : Area (∆Def) - Mathematics

Sum

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)

 

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Solution

GIVEN: ΔABC and ΔDEF are two triangles such that .

\[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\]

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`

Concept: Triangles Examples and Solutions
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Q 13 | Page 129
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