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Grade 12th PassAnalytical Geometry

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?

Profile image of Charitha Gorrela
9 Years agoGrade 12th Pass
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1 Answer

Profile image of Shahid
ApprovedApproved Tutor Answer9 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}

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