7. Complete the following activity to find the length of median AQ on side BC if AB2 + AC2 = 122 and BQ = 5. - A B Q С
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In the given figure, AB
2
+AC
2
=122, BC=10. Find the length of the median on side BC.
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Correct option is A)
In ΔABC, seg AQ is a median
∴ BQ=
2
1
BC=
2
1
×10
BQ=5
By Appollonius theorem,
AB
2
+AC
2
=2AQ
2
+2BQ
2
122=2AQ
2
+2(5)
2
122=2AQ
2
+2×25
122=2AQ
2
+50
122−50=2AQ
2
72=2AQ
2
2
72
=AQ
2
36=AQ
2
AQ=6
∴ The length of the median is 6 units.
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