Question : In the isosceles triangle ABC with BC is the unequal side of the triangle, and line AD is the median drawn from the vertex A to the side BC. If the length AC = 5 cm and the length of the median is 4 cm, then find the length of BC (in (cm).
Option 1: 5
Option 2: 3
Option 3: 4
Option 4: 6
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Correct Answer: 6
Solution : Given: $\Delta ABC$ is an isosceles triangle Hence, AB = AC = 5cm From Apollonius's theory, we get, ⇒ $5^2+5^2=2(4^2+DC^2)$ ⇒ $25+25=16+DC^2$ ⇒ $DC^2=9$ ⇒ $DC = 3\ \text{cm} $ Since D is the median point on the side BC. $\therefore BD = DC = 3\ \text{cm}$ $BC=BD+CD$ ⇒ $BC = 3+3=6\ \text{cm}$ Hence, the correct answer is 6.
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