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Question

In ΔABC, 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.

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Solution

Let Δ ABC is similar to Δ ADE

angle A is common

angle B = angle D ( BCDE, corresponding angle are equal)

triangle are similar

thus by proportional property of similar triangles

ABAD=ACAE=BCDE

or (AD+DB)AD=BCDE and (AE+EC)AE=BCDE

or 1+DBAD=BCDE and 1+ECAE=BCDE

putting values of AD, BC, DE and AE

1+DB2.4=52and1+EC3.2=52

1+DB2.4=2.5and1+EC3.2=2.5

DB2.4=2.51andEC3.2=2.51

\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


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