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diagonal distance in squares

 May 28, 2017
 #1
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To find the length of the diagonal of a square, multiply the length of one side by the square root of 2: If the length of one side is x... The central angle of a square: The diagonals of a square intersect (cross) at a 90-degree angle.

 May 28, 2017
 #2
avatar+99282 
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use pythagoras's theorum

 

\(d^2=l^2+b^2\)

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 May 28, 2017
 #3
avatar+99282 
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oh it is a square so length l and breadth b will be the same

 

\(d^2=2l^2\\ d=\sqrt{2l^2}\;\;units\)

Melody  May 28, 2017
 #4
avatar+2340 
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\(\sqrt{2l^2}=l\sqrt2\)

 

\(\sqrt{2l^2}\)

 

This can be simplified further:

 

Im going to use a radical rule that says \(\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\hspace{1cm}\), assuming \(a\geq0,b\geq0\). You might notice that there is a condition for using this. This rule only works when both a and b are nonnegative. In the context of geometry, \(l\) should be positive because otherwise a square couldn't exist if a side length is -8, for example. I will apply this rule:

 

\(\sqrt{2l^2}=\sqrt{2}\sqrt{l^2}\)

 

Here, too, I will apply a rule that only works with nonnegative numbers: \(\sqrt[n]{a^n}=a\), assuming \(a\geq0\). Let's apply it now:

 

\(\sqrt{2}\sqrt{l^2}=\sqrt{2}*l=l\sqrt{2}\).

 

I just wanted you to be aware of this. You can't simplify \(\sqrt{2l^2}\)   further otherwise.

TheXSquaredFactor  May 28, 2017

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