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प्रश्न
In a ΔABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4cm, AE = 3.2 cm, DE = 2cm and BC = 5 cm, find BD and CE.
उत्तर
We have,
DE || BC
Now, In ΔADE and ΔABC
∠A = ∠A [common]
∠ADE = ∠ABC [∵ DE || BC ⇒ Corresponding angles are equal]
⇒ ΔADE ~ ΔABC [By AA criteria]
`rArr"AB"/"BC"="AD"/"DE"`
`rArr"AB"=(2.4xx5)/2`
⇒ AB = 1.2 × 5 = 6.0 cm
⇒ AB = 6 cm
∴ BD = 6 cm
BD = AB – AD
= 6 – 2.4 = 3.6 cm
⇒ DB = 3.6 cm
Now,
`"AC"/"BC"="AE"/"DE"` [∵ Corresponding sides of similar triangles are equal]
`rArr"AC"/5=3.2/2`
`rArr"AC"=(3.2xx5)/2=1.6xx5=8.0 ` cm
⇒ AC = 8 cm
∴ CE = AC – AE
= 8 – 3.2 = 4.8 cm
Hence, BD = 3.6 cm and CE = 4.8 cm
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