Sections A – Data Interpretation and Quantitative Ability

11. In an equilateral triangle ABC, whose length of each side is 3 cm, D is a point on BC such that BD = 1/2 CD. What is the length of AD?

A. cm B. cm C. cm D. cm E. None of the above

Solution:

It is given that BD = CD.

Given that BC = 3

Þ BD + CD = 3

Þ BD + 2BD = 3

Þ BD = 1 and CD = 2

Let us drop a perpendicular AE to BC meeting BC at E.

Now BE = EC = cm [∵ ABC is an equilateral triangle].

In DAEC, AC² - EC² = AE² ® (1) and

In DADE, AD² - DE² = AE² ® (2)

Equating (1) and (2), we get AC² - EC² = AD² - DE²

Or. AC² - AD² = EC² - DE²

Or. AC² - AD² = (EC + DE) (EC - DE)

Or, AC² - AD² = (CD) (BD)

[∵EC = BE and BE - DE = BD]

Or, 3² - AD² = (2) (1)

Or, AD = cm. Choice (C)