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

Question

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

Philoid · Accepted Answer

In the figure given below,

Given: AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm

Let BD be x cm and CE be y cm,

Then, from, ΔADE and ΔABC, we can write,

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

Or $\frac{AD}{AD+BD}=\frac{DE}{BC}$

or $\frac{2.4}{2.4+x}=\frac{2}{5}$

or 12 = 4.8 + 2x

or x = 7.2/2

or x = BD = 3.6cm

Similarly, from ΔADE and ΔABC, we can write,

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

Or $\frac{AE}{AE+EC}=\frac{DE}{BC}$

or $\frac{3.2}{3.2+y}=\frac{2}{5}$

or 16 = 6.4 +2y

or y = 9.6/2

or y = CE = 4.8 cm

Thus, the lengths of BD and CE are 3.6 cm and 4.8 cm respectively.