In the figure given above, if DE ∥BC, then the value of x equals to

Given that DE

∥

BC.

△ ADE

and

△ ABC

∠ ADE = ∠ ABC

(As

DE ∥ BC

) (Corresponding angles are equal)

∠ AED = ∠ ACB

(As

DE ∥ BC

) (Corresponding angles are equal)

∠ DAE = ∠ BAC

(common angle)

△ ADE ~ △ ABC

(By AAA rule)
Now, if two triangles are similar, then their corresponding sides are proportional.

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

\Rightarrow \frac{3}{2 + 3} = \frac{4}{x}

\Rightarrow x = 6.7 cm

.
Therefore, the value of

x is 6.7 cm

.
Hence option 4 is the answer.

In the figure given above, if DE $∥$ BC, then the value of x equals to