Question

In triangle ABC,D and E are points on sides AB and AC respectively such that DE parallel to BC and AD:DB=5:4. DC and BE intersect at F. Find area(triangleDFE) .

area(triangleCFB)

Answer 1

In triangle ABC,

DE||BC

triangle ADE is similar to triangle ABC

Therefore, AD/AB = DE/BC

5/9 = DE/BC -Equation 1

In triangle DEF and BFC

angle EDF = angle BCF (alternate angles)

angle DFE = angle CFB (vertically opposite angles)

so, triangle DEF is similar to triangle BFC

Therefore, arDEF/arBFC

DE square/BC square = 5*5/9*9

=25/81  

Answer 2

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