Question

In the given figure, if angle ADE = angle B, and AD= 6.8 cm, AE = 8.6 cm, BE = 2.4 cm and BC = 5.5 cm, then the value of DE is​

Answer 1

• ∠A is common in both the triangles i.e. △ADE and △ABC

Also,

• ∠ADE=∠B

Since, two angles of triangles △ADE and △ABC

are equal, therefore,

△ADE∼△ABC

Using properties of similar triangles, we have :

AD/AB = DE/BC

AD/AE+EB =DE/BC

6.8/8.6+2.4= DE/5.5

DE= 6.8/2 =3.4 cm

Answer 2

Given:

∠A is common in both the triangles, △ADE and △ABC.

∠ADE=∠B

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

△ADE∼△ABC

properties of similar triangles

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

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

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

$\mathrm{DE}=\frac{6.8}{2}$

DE=3.4 cm

Hence the value of DE is​ 3.4 cm