If the extremities of a diagonal of a square | vedclass

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(C) Let the side of the square be $a$.In a square, the length of the diagonal $d$ is related to the side $a$ by the formula $d = a\sqrt{2}$, or $d^2 =

Vedclass · Accepted Answer

$\sqrt{15}$

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(C) Let the side of the square be $a$.In a square, the length of the diagonal $d$ is related to the side $a$ by the formula $d = a\sqrt{2}$, or $d^2 = 2a^2$.The extremities of the diagonal are given as $A(1, 2, 3)$ and $C(2, -3, 5)$.The length of the diagonal $AC$ is calculated using the distance formula:$AC = \sqrt{(2-1)^2 + (-3-2)^2 + (5-3)^2}$$AC = \sqrt{1^2 + (-5)^2 + 2^2}$$AC = \sqrt{1 + 25 + 4} = \sqrt{30}$Since $AC^2 = 2a^2$, we have:$(\sqrt{30})^2 = 2a^2$$30 = 2a^2$$a^2 = 15$$a = \sqrt{15} 	ext{ units}$.

If the extremities of a diagonal of a square are $(1, 2, 3)$ and $(2, -3, 5)$, then its side is of length

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