Math, asked by AnnikaDavis, 1 year ago

$prove \: yourself \: brainlians$
D and E are points on the sides AB and AC respectively of triangle ABC such that DE||BC and AD:DB=4:5.CD and BE intersect each other at F. Find the ratio of the areas of triangle DEF and triangle CBF.

blackpinf4ever: Anneyonghaseyo

AnnikaDavis: Anneyoung

blackpinf4ever: Army?

akshaywalke35: DE || BC and AD : DB = 5 : 4

Now, ∠ADE = ∠ABC and ∠AED = ∠ACB [Corresponding angles]

In △ ADE and △ ABC, we have

∠ADE = ∠ABC,

∠AED = ∠ACB and

∠A = ∠A [Common]

So, △ ADE ~ △ ABC [By AAA similarity]

⇒

Given,

⇒

Now, adding 1 on both sides,we get

⇒

or

Again, In △ DEF and △ BCF, we have

∠EDF = ∠BCF [Alternate interior angles]

∠DFE = ∠BFC [Vertically opposite angles]

and ∠DEF = ∠FBC [Alternate interior angles]

So, △ DEF ~ △ BCF [By AAA similarity

Answers

Answered by blackpinf4ever

△ADE∼△ABC

∴∠D=∠B

&∠E=∠C

∠A is common.

So,

AD/AB=AE/AC=DE/BC=49

Now, In△DEF and △BFC

∠D=∠C and

∠B=∠E

So, △DEA∼ △BFC

In similar triangles ratio of areas is equal to the ratio of square of corresponding sides.

area of area of △DEFarea of △BFC=DE2BC2

=42/92=16/81

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D and E are points on the sides AB and AC respectively of triangle ABC such that DE||BC and AD:DB=4:5.CD and BE intersect each other at F. Find the ratio of the areas of triangle DEF and triangle CBF.​

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$prove \: yourself \: brainlians$
D and E are points on the sides AB and AC respectively of triangle ABC such that DE||BC and AD:DB=4:5.CD and BE intersect each other at F. Find the ratio of the areas of triangle DEF and triangle CBF.