Question

In figure, DE||BC, then the value of x equals to:

• A. 2.5 cm
• B. 2 cm
• C. 1.4 cm
• D. 4 cm

Answer 1

Answer: (B)

2 cm

Given that,

$DE\parallel BC$.

To find out,

The value of $x$.

In $△ADE$ and $△ABC$

$\angle ADE=\angle ABC$ [Corresponding angles]

$\angle AED=\angle ACB$ [Corresponding angles]

$\angle DAE=\angle BAC$ (common angle)

Hence, by AAA criteria

$△ADE\sim △ABC\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}\frac{1.5}{4.5}=\frac{1}{1+x}1+x=3$

$x=2$.

Hence, the value of $x$ is $2$.