Question

In fig if $\angle ADE=\angle ABC$ ,then show that $△ADE\sim △ABCand$ AD=6.8 cm, AE =8.6 cm, BE=2.4 cm and BC = 5.5 cm Find DE

• A. $5.4$ cm
• B. $4.6$ cm
• C. $3.4$ cm
• D. None of these

Answer 1

Answer: (C)

$3.4$ cm

Consider the diagram given in the question.

$\angle A$ is common in both the triangles, $△ADE$ and $△ABC$.

Also,

$\angle ADE=\angle B$

Since, two angles of triangles $△ADE$ and $△ABC$ are equal, therefore,

$△ADE\sim △ABC$

Using properties of similar triangles, we have

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

$\frac{AD}{AE+EB}=\frac{DE}{BC}$

$\frac{6.8}{8.6+2.4}=\frac{DE}{5.5}$

$DE=\frac{6.8}{2}=3.4cm$

Hence, $DE$ is $3.4cm$.