Question

In triangle ABC if AD=DB and AE=EC, if BC =5.6cm, then find the value of DE

Answer 1

2.8

OK I guess you don't know

Answer 2

Given,

In ΔABC,

$AD=DB\\AE=EC$

$BC=5.6cm$

To find,

Value of $DE$.

Solution,

Let the side $DE$ of the triangle be $x$.

In ΔABC and ΔADE,

$AD=\frac{1}{2}AB$

⇒$\frac{AD}{AB}=\frac{1}{2}$       ------(i)

Similarly,

$AE=\frac{1}{2}AC$

⇒$\frac{AE}{AC}=\frac{1}{2}$      ------ (ii)

From equation (i) and (ii),

$\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{2}$

Also,

In ΔABC and ΔADE,

∠A is common.

Hence, by SAS property of similarity, both the triangles are similar.

⇒$\frac{AD}{AB}= \frac{AE}{AC}= \frac{DE}{BC}= \frac{1}{2}$

This is because, in similar triangles ratio of the sides is equal.

Using above results,
⇒$\frac{DE}{BC} =\frac{1}{2}$

⇒$\frac{x}{5.6} =\frac{1}{2}$

⇒$2x=5.6$

⇒$x=\frac{5.6}{2}$

⇒$x=2.8cm$

Therefore, the length of DE is $2.8cm$.