Question

In $\Delta ABC$, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4 = 3.2 cm, DE= 2cm and BC= 5cm, find BD and CE.

Answer 1

Let $\Delta ABC$ is similar to $\Delta ADE$

angle A is common

angle B = angle D ( $\frac{BC}{DE}$, corresponding angle are equal)

$\therefore$ triangle are similar

thus by proportional property of similar triangles

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

or $\frac{(AD+DB)}{AD}=\frac{BC}{DE}$ and $\frac{(AE+EC)}{AE}=\frac{BC}{DE}$

or $1+\frac{DB}{AD}=\frac{BC}{DE}$ and $1+\frac{EC}{AE}=\frac{BC}{DE}$

putting values of AD, BC, DE and AE

$1+\frac{DB}{2.4}=\frac{5}{2}and1+\frac{EC}{3.2}=\frac{5}{2}$

$1+\frac{DB}{2.4}=2.5and1+\frac{EC}{3.2}=2.5$

$\frac{DB}{2.4}=2.5-1and\frac{EC}{3.2}=2.5-1$

\frac{DB}{2.4} = 1.5 and \frac{EC}{3.2} = 1.5

\frac{DB} = 1.5*2.4 and EC = 1.5*3.2

DB=3.6 cm and EC=4.8 cm ans