Question

In the given figure, $DE \parallel BC$ in $\triangle ABC$ such that BC = 8 cm, AB = 6 cm and DA = 1.5 cm. Find DE.

Answer 1

Answer:

The Length of DE is 2 cm.

Step-by-step explanation:

Given:

In ∆ABC, DE || BC

BC = 8 cm , AB = 4cm , DA = 1.5 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]

8/DE = 6/1.5

6 DE = 8 × 1.5  

6 DE = 12

DE = 12/6  

DE = 2 cm  

Hence, the Length of DE is 2 cm.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

$\huge\mathcal{SOLUTION}$

GIVEN :

♤$<strong> </strong>DE \parallel BC$

♤ BC = 8 cm

♤ AB = 6 cm

♤ DA = 1.5 cm

♤ DE = ??

SOLVE :

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

∠ABC = ∠ADE (corresponding angles )

and ∠A = ∠A (common)

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

[By AA similarity ]

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

[Corresponding sides of similar triangles are proportional]

$\frac{8}{DE}= \frac{6}{1.5 }$

=> 6 DE = 8 × 1.5

=>6 DE = 12

=> DE = 2

Hence , The value of DE is 2 cm .