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# if the extremities of a diagonal of a square are (1,2,3) and (2,-3,5) then the length of it’s side is?

Shahid
74 Points
4 years ago
Dear Charitha ,
I want you to note that it’s a Cube , not a square which is formed by those points.(Because it’s in 3D Geometry)
Now,
Given:- Let A (1,2,3) and E (2,-3,5) be the Extrimities of the given “Cube”.(say,ABCDEFGH)
To Find:- The Length of the side of the cube.
Solution:
First, let us Find the length AE.
AE = $\sqrt{(2 - 1)^{2} + (2 - (-3))^{2} + (3 - 5)^{2}))}\sqrt{}$
AE = $\sqrt{30}$

Here , AE is the Body Diagonal.
And Let AB be a Side of the cube.
Let length of AB = a

Now By Solving , We get that AE = $\sqrt{3}$ x a
$\therefore$ AE = $3 \sqrt{10}$