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Home » D and E are points on the sides AB and AC respectively of a ∆ABC such that DE║BC. (i) If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC. (ii) If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.
D and E are points on the sides AB and AC respectively of a ∆ABC such that DE║BC. (i) If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC. (ii) If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.
CBSE | Class 10 | Exercise 4A | Maths | RS Aggarwal | Triangles
D and E are points on the sides AB and AC respectively of a ∆ABC such that DE║BC. (i) If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC. (ii) If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.

 

 

(i)

In ∆ ABC,

DE ∥ BC.

Applying Thales’ theorem,

\frac{{AD}}{{DB}} = \frac{{AE}}{{EC}}

∵ AD = 3.6 cm , AB = 10 cm, AE = 4.5cm

∴ DB = 10 − 3.6 = 6.4cm

\begin{array}{l} \frac{{3.6}}{{6.4}} = \frac{{4.5}}{{EC}}\\ EC = \frac{{6.4 \times 4.5}}{{3.6}}\\ EC = 8cm\\ \\ AC = AE + EC\\ AC = 4.5 + 8\\ \therefore AC = 12.5cm\\ \end{array}

(ii)

In ∆ ABC,

DE || BC

Applying Thales’ Theorem,

\frac{{AD}}{{DB}} = \frac{{AE}}{{EC}}

Add 1 to both sides,

\begin{array}{l} \frac{{AD}}{{DB}} + 1 = \frac{{AE}}{{EC}} + 1\\ \frac{{AB}}{{DB}} = \frac{{AC}}{{EC}}\\ \frac{{13.3}}{{DB}} = \frac{{11.9}}{{5.1}}\\ DB = \frac{{13.3 \times 5.1}}{{11.9}}\\ DB = 5.7cm\\ \\ AD = AB - DB\\ AD = 13.5 - 5.7\\ \therefore AD = 7.6cm\\ \end{array}

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