In the isosceles triangle ABC with BC being 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).
Answer & explanation
Correct answer: option 2
Since \(\Delta \)ABC is an isosceles triangle,
Therefore, AB = AC = 5 cm
Apply Apollonius' theorem
= \( {5 }^{2 } \) + \( {5 }^{2 } \) = 2(\( {4 }^{2 } \) + \( {DC }^{2 } \))
= 25 + 25 = 2(16 + \( {DC }^{2 } \))
= 50 = 2(16 + \( {DC }^{2 } \))
= 25 = 16 + \( {DC }^{2 } \)
= \( {DC }^{2 } \) = 25 - 16
= \( {DC }^{2 } \) = 9
= DC = 3 cm
Since D is he median point on the side BC,
Therefore, BD = DC = 3 cm
= BC = BD + CD
= BC = 3 + 3 = 6 cm
Therefore, BC is 6 cm.