Question

In ΔABC, point M is the midpoint of side BC. If, AB²+AC²= 290 cm²,AM=8cm, find BC.

Answer 1

therefore BM = 9 CM
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HOPE IT WILL HELP U

Answer 2

Given :

In ∆ABC , point M is the midpoint of

side BC .

AB² + AC² = 290 cm² ,

AM = 8 cm

BC= ?

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By Appolonius Theorem :

The sum of the Squares of two sides

of a triangle is equal to twice the

square on half the third side plus

twice the square on the median which

bisects the third side .

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Here ,

AB² + AC² = 2( BM² + AM² )

=> 290 = 2( BM² + 8² )

=> 145 = BM² + 64

=> 145 - 64 = BM²

=> 81 = BM²

=> 9² = BM

=> 9 = BM

Now ,

BC = BM + MC

=> BC = BM + BM

[ Since , M is midpoint of BC ]

=> BC = 2BM

BC = 2 × 9

BC = 18

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