Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB = $\sqrt{200}$ , BC= $\sqrt{208}$ , AC= $\sqrt{8}$ , Since AB+BC>AC, points A, B and C from a triangle.

Reason: If $B C^{2} = A B^{2} + A C^{2}$ , then $Δ A B C$ is a right triangle, right angled at A.

If both assertion and reason are true and reason is te correct explanation of assertion

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If both assertion and reason are true but reason is not the correct explanation of assertion.

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If assertion is true but reason is false.

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If assertion is false but reason is true.

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Solution

The correct option is B If both assertion and reason are true but reason is not the correct explanation of assertion.

Sum of the two sides is greater than third side
$∴ A B + B C > A C a n d A B + A C > B C$
$∵$ ABC is a triangle
Also $B C^{2} = A B^{2} + A C^{2}$
$(\sqrt{208})^{2} = (\sqrt{200})^{2} + {\sqrt{8}}^{2} 208 = 200 + 8 208 = 208$
$∴$ ABC is right angled triangle
Assertion: True; Reason: True but is not the correct explanation of assertion

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Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB =√200, BC= √208, AC= √8, Since AB+BC>AC, points A, B and C from a triangle. Reason: If BC2=AB2+AC2, then ΔABC is a right triangle, right angled at A.

Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB = $\sqrt{200}$ , BC= $\sqrt{208}$ , AC= $\sqrt{8}$ , Since AB+BC>AC, points A, B and C from a triangle.

Reason: If $B C^{2} = A B^{2} + A C^{2}$ , then $Δ A B C$ is a right triangle, right angled at A.