Question

In the following figure DE is parallel to BC, AD=1cm
BD = 3cm and Bc=6cm.The length Of DE is equal
to:
​

Answer 1

Here is the detailed answer.

Answer 2

Given :- DE || BC , AD=1cm , BD = 3cm and Bc=6cm.

To Find :- DE = ?

Solution :-

In ∆ABC and ∆ADE we have,

→ ∠ABC = ∠ADE { since DE || BC , corresponding angles }

→ ∠BAC = ∠DAE { Common }

So,

→ ∆ABC ~ ∆ADE { By AA similarity }

then,

→ AB/AD = BC/DE { when two ∆'s are similar , their corresponding sides are in same ratio . }

→ (AD + BD)/AD = BC/DE

→ (1 + 3)/1 = 6/DE

→ 4/1 = 6/DE

→ 4DE = 6

→ DE = (6/4)

→ DE = (3/2)

→ DE = 1.5 cm (Ans.)

Hence, Length of DE is equal to 1.5 cm .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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