Question

In $\triangle ABC$, D and E are points on side AB and AC respectively such that $DE \parallel BC$and AD : DB = 3 : 1. If EA = 3.3 cm, then AC =
(a) 1.1 cm
(b) 4 cm
(c) 4.4 cm
(d) 5.5 cm

Answer 1

Answer:

AC is 4.4 cm

Among the given options option (c) is 4.4 cm is the correct answer.

Step-by-step explanation:

Given:

In ΔABC, points D and E lie on AB and AC.

DE || BC

AD : BD = 3 : 1

EA = 3.3 cm.

AD/AB = AE/AC

[By using  corollary of the Basic Proportionality theorem]

AD/(AD + BD) = 3.3/AC

3.3/AC = AD/(AD + ⅓ AD]

[AD/BD = 3/1 , BD = ⅓ AD]

3.3/AC = AD/(3AD + 1AD)/3

3.3/AC = AD/4AD/3

3.3/AC = 1/(4/3)

AC = 3.3 × 4/3

AC = 1.1 × 4

AC = 4.4 cm

Hence, the Length of AC is 4.4 cm

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Answer 2

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