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Home » In ∆ABC, DE ║ BC such that . If AC = 5.6cm, then AE = ? (a) 4.2cm (b) 3.1cm (c) 2.8cm (d) 2.1cm
In ∆ABC, DE ║ BC such that \begin{array}{l} \frac{{AD}}{{DB}} = \frac{{3}}{{5}}\\ \end{array}. If AC = 5.6cm, then AE = ? (a) 4.2cm (b) 3.1cm (c) 2.8cm (d) 2.1cm
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
In ∆ABC, DE ║ BC such that \begin{array}{l} \frac{{AD}}{{DB}} = \frac{{3}}{{5}}\\ \end{array}. If AC = 5.6cm, then AE = ? (a) 4.2cm (b) 3.1cm (c) 2.8cm (d) 2.1cm

Correct Answer: (d) 2.1 cm

Explanation:

 

 

 

Given,

DE || BC.

Applying Thales’ theorem,

\begin{array}{l} \frac{{AD}}{{DB}} = \frac{{AE}}{{EC}}\\ \end{array}

AE be x cm.

EC = (5.6 – x) cm

\begin{array}{l} \frac{{3}}{{5}} = \frac{{x}}{{5.6-x}}\\ \end{array}

3 (5.6 − ????) = 5????

16.8 − 3???? = 5????

8???? = 16.8

x = 2.1 cm

i

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