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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