Question

In the given figure, $DE \parallel BC$ and $AD= \frac {1}{2}$ BD. If BC = 4.5 cm, find DE.

Answer 1

Answer:

The Length of DE is 1.5 cm.

Step-by-step explanation:

Given:

In ∆ABC, DE || BC

AD = ½ BD , BC = 4.5 cm  

In ∆ABC and ΔADE,

∠B =   ∠ADE                                 (Corresponding angles)

∠A = ∠A                                         (Common)

∆ABC ∼ ΔADE                           (By AA similarity criterion)

BC/DE = AB/AD

[Corresponding sides of similar triangles are proportional]

BC/DE = AB/AD

4.5/DE = (AD + BD)/AD

4.5/DE = (½ BD + BD)/ ½  BD

4.5/DE = (1BD + 2BD)/2 / ½ BD  

4.5/DE = 3/2 BD / ½ BD  

4.5/DE = 3/2 / ½  

4.5/DE = 3/2  × 2/1

4.5/DE = 3

3 DE = 4.5

DE = 4.5/ 3

DE = 1.5 cm

Hence, the Length of DE is  1.5 cm

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Answer 2

$\huge\mathfrak {Solution}$

GIVEN :

☆ $DE \parallel BC$

☆ $AD= \frac {1}{2}$ BD.

☆ BC = 4.5 cm

☆ DE = ??

SOLVE :

In $\triangle ABC$ And $\triangle ADE$,

∠ABC =∠ADE (corresponding angles )

∠BAC = ∠DAE (common )

=> $\triangle ABC$ $\sim$ $\triangle ADE$

(By AA similarity criterion )

$\frac{BC}{DE} = \frac{AB}{AD}$

[Corresponding sides of similar triangles are proportional]

=> $\frac{BC}{DE} = \frac{AD + BD }{AD}$

=> $\frac{4.5}{DE}$= (1/2BD + BD )/ 1/2 BD

=> $\frac{4.5}{DE}$ = [BD ( 1/2 + 1 )]/1/2 BD

=> $\frac{4.5}{DE} = (3/2) ÷ (1/2)$

=> $\frac{4.5}{DE} = 3$

=> DE = 4.5 / 3

=> DE = 1.5

Hence , The value of DE is 1.5 cm .