Question

in triangle ABC,point M is the midpoint of side BC.If ,AB^2+AC^2=290 cm^2,AM=8 cm,find BC

Answer 1

Answer: The length of BC is 18 cm.

Step-by-step explanation:

Given:- I) In ΔABC, AM is median bisecting side BC at point M.

            II) $AB^{2} + AC^{2} = 290  cm^{2}$

            III) AM = 8 cm

Theorem Used:- APOLLONIUS THEOREM-> It states that sum of squares of any two sides of any triangle equals twice the square on half the third side, together wih twice the square on the median bisecting the third side.

Solution:- In ΔABC,

By Apollonius Theorem

=>$AB^{2} + AC^{2} = 2(AM^{2} + BM^{2})$

=> 290 = 2( 8² + BM²)  [ ∵AB²+AC²=290 ....given]

=> $\frac{290}{2} = 8^{2} + BM^{2}$

=> 145 = 64 + BM²

=>BM²=145-64

=>BM²= 81

=>BM=√81

=>BM= 9 cm

BC= 2BM (∵Median AM bisects BC at point M)

    =2×9

    =18 cm

==> Length of BC is 18 cm.

Answer 2

Answer:

bc = 18cm

Step-by-step explanation:

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