Question

In \(\triangle ABC\), if \(DE \parallel BC\), \(AE/CE = 3/5\) and \(AB = 5.6\) cm, then \(AD =\):

• A. 2.8 cm
• B. 2.1 cm
• C. 3 cm
• D. 2.4 cm

Hint:

In problems involving parallel lines and triangles, use the Basic Proportionality Theorem (Thales' theorem) to relate the corresponding sides of the triangle.

Answer 1

The Correct Option is A

In a triangle, if a line parallel to one side divides the other two sides in a given ratio, then by the Basic Proportionality Theorem (also known as Thales’ theorem), we have: \[ \frac{AE}{CE} = \frac{AB}{BC} \] We are given that \(\frac{AE}{CE} = \frac{3}{5}\), and \(AB = 5.6\) cm. Therefore: \[ \frac{AB}{BC} = \frac{3}{5} \] Let \(BC = x\). Then: \[ \frac{5.6}{x} = \frac{3}{5} \] Cross-multiplying: \[ 5.6 \times 5 = 3 \times x \quad \Rightarrow \quad x = \frac{28}{3} \approx 9.33 \] Now, using the relation \(\frac{AD}{AB} = \frac{AE}{AB}\): \[ AD = \frac{AE}{AB} \times AB \] Thus, the correct answer is option (1), \(AD = 2.8\) cm.