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SSC CHSL 2024 PYQ — Question 69

SSC CHSL - 01 July 2024 - Shift 3 • Quantitative Aptitude • Q69

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In a triangle ABC, AB = 6 units, BC = 8 units, and AC = 10 units. Let M be a point on AC such that BM = 5 units. With a point D, a triangle BMD is formed and the triangle BMD is similar to the triangle ABC with BMAB=BDAC\frac{BM}{AB}=\frac{BD}{AC}. What is the length of BD in units?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 253\frac{25}{3}.

Since △BMD is similar to △ABC, the corresponding sides are proportional. The ratio is given as:

BM/AB = BD/AC

According to the question:

⇒ 5/6 = BD/10

⇒ 5 × 10 = 6 × BD

BD = 50/6 = 25/3 units