In $$\triangle$$ABC, D and E are the points on sides AC and AB, respectively, such that $$\angle$$ADE = $$\angle$$B. If AD =7.6 cm, AE = 7.2 cm, BE = 4.2 cm and BC = 8.4 cm,then DE is equal to:

given. AD=7.6cm

            AE=7.2cm

             BE=4.2cm

             BC=8.4cm

In ∆ADE and ∆ABC

∠A=∠A. ( common)

∠ADE=∠ABC (given)

∆ADE~∆ABC. (AA similarity)

$$\frac{AD}{AB}$$=$$\frac{DE}{BC}$$.  { Ratio of the corresponding sides of the similar triangles are equal}

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

$$\frac{7.6}{7.2+4.2}$$=$$\frac{DE}{8.4}$$

$$\frac{7.6}{11.4}$$=$$\frac{DE}{8.4}$$

DE=$$\frac{7.6×8.4}{11.4}$$

Hence DE=5.6cm