Question

In the given figure, if DE || BC, then find the ratio of​

Answer 1

The ratio will be 4/12 when simplified gives:
1/3 that is 1:3
So the ratio will be 1:3

Answer 2

Answer:

The ratio is 1 : 8.

Step-by-step explanation:

Given:

In ΔABC,  

DE∣∣BC  

and DE = 4cm and BC = 12cm  

To find:  ar(DECB)/ar(ΔADE)    

Sol. In ΔABC and ΔADE  

DE∣∣BC [GIven]

(corresponding angle) ⇒∠1 =∠2

                                      ⇒∠3 =∠4

∴ABC∼ΔADE  [By AA similarity criterion]

Now,  

ar(ΔADE)/ar(ΔABC) =( DE/BC )²

(∵ Ratio of the two similar triangle is equal to the squares of the ratio of their corresponding sides)

⇒ ar(DECB)+ar(ΔADE)/ar(ΔADE) = (12/4)²  

ar(ΔADE)/ar(DECB)+ar(ΔADE)/ar(ΔADE)=(3)²  

ar(ΔADE)/ar(DECB) + 1 = 9  

ar(ΔADE)/ar(DECB) = 9 − 1 = 8

ar(DECB)

ar(DECB)/ar(ΔADE)  =  1/8  

Hence, the required ratio is 1 : 8.

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