Question

★ELLOH




$\large\mathbf{HEY\: QUESTION❤}$



In the given figure, if DE || BC, AE = 8 cm, EC = 2 cm and BC = 6 cm, then find DE

★ FIG IN ATTACHMENT

★ REQUIRED QUALITY ANSWER​

Answer 1

Answer:

Go through the attachment buddy

Step-by-step explanation:

Hope it helps u

Answer 2

Given:

• DE || BC
• AE = 8 cm
• EC = 2 cm
• BC = 6 cm

To find:

→ DE = ?

Solution:

In ΔADE and ΔABC,

∠A = ∠A            (Common angle)

∠ADE = ∠ABC  (Corresponding angles)

By AA similarity,

ΔADE ∼ ΔABC

So, their corresponding sides are proportional.

$\sf{\dfrac{AE}{AC} = \dfrac{DE}{BC}}\\\\\\\Rightarrow \: \sf{\dfrac{8}{AE+EC} = \dfrac{DE}{6}}\\\\\\\\\Rightarrow \: \sf{\dfrac{8}{8+2} = \dfrac{DE}{6}}$

$\Rightarrow \: \sf{\dfrac{8}{10} = \dfrac{DE}{6}}\\\\\\\Rightarrow \: \sf{10 \times DE = 8 \times 6}\\\\\\\Rightarrow \: \sf{10 \times DE = 48}\\\\\\\Rightarrow \: \sf{DE = \dfrac{48}{10}}\\\\\\\\\therefore \large{\boxed{\boxed{\bf{DE = 4.8 \: cm}}}}$