Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minai-gemini

MathematicsMediumsingle choice

In a triangle ABC, if $a = 6$ , $b = 8$ , $c = 10$ , find the length of the median from vertex A to side BC.

Options:

Answer:

Solution:

The length of the median $m_{a}$ from vertex A to side BC is given by the formula $m_{a}^{2} = \frac{2 b ^{2} + 2 c ^{2} - a ^{2}}{4}$ . Substituting the given side lengths, $m_{a}^{2} = \frac{2 ( 8 ^{2} ) + 2 ( 1 0 ^{2} ) - 6 ^{2}}{4} = \frac{2 ( 64 ) + 2 ( 100 ) - 36}{4} = \frac{128 + 200 - 36}{4} = \frac{328 - 36}{4} = \frac{292}{4} = 73$ . Therefore, the length of the median $m_{a} = 73$ .

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points

⏱ 2mℹ️ Source: ai-gemini

Doubts & Discussion

Loading discussions...