In $△ A B C$ , AP is the median. If $A P = 7$ and $A B^{2} + A C^{2} = 260$ , then find BC.

14

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Solution

The correct option is D $18$ cm
By Apollonius Theorem (states that "the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side".) , we have

$B C^{2} = A B^{2} + A C^{2} + 2 A P^{2}$

$B C^{2} = 260 + 2 (7)^{2}$

$B C^{2} = 260 + 98 = 358$

$B C = 18.92$

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Similar questions

△ A B C

A P

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{A B}^{2} + {A C}^{2} = 260

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△ A B C

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B C = 18, A B^{2} + A C^{2} = 260

The area of following triangle is 30 cm². If BC = 5 cm then AP = ?

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A P

A P = 12, A B^{2} + A C^{2} = 320

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