Question

I challenge You all to solve this question. What is the Ratio in above question? Whoever will solve this I will mark him Brainliest.

Answer 1

HELLO FRIEND,

HERE IS YOUR SOLUTION,

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]

⇒AD/AB=DE/BC

Given,AD/BD=5/4

⇒BD/AD=4/5

Now, adding 1 on both sides,we get

BD/AD +1 = 4/5 +1

⇒AB/AD = 9/5 = DE/BC

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]

⇒ar(tri. DEF)/ ar(tri. BCF) = (DE/BC)^(2)

⇒ = (5/9)^(2)

⇒ = 25/81

I HOPE IS WILL HELPFUL TO YOU

I M' SO SORRY MODERATOR, I DIDN'T SEE WHAT IS GIVEN BUT TO SOLVE THIS ALL THE PROCESS IS SAME AND SAME THING TO DO ANOTHER QUE. TOO WHICH IS LIKE THIS ......