Exams › SSC CGL (Prelims) › General

A right-angled triangle ABC (\(\angle B = 90^\circ\)) has sides AB = 8 cm and BC = 15 cm. A perpendicular BD is dropped onto the hypotenuse AC. Find the length of AD.

1. 3.76 cm
2. 3.01 cm
3. 4.12 cm
4. 5.24 cm

Correct answer: 3.76 cm

Solution

The hypotenuse is \(AC = \sqrt{8^2 + 15^2} = 17\) cm. Using the property of a right triangle with altitude to the hypotenuse, \(AB^2 = AD \cdot AC\). Hence \(AD = \frac{8^2}{17} = \frac{64}{17} \approx 3.76\) cm.

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