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# how do you calculate the diagonal distance in a square?

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diagonal distance in squares

Guest May 28, 2017
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#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.

Guest May 28, 2017
#2
+90544
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use pythagoras's theorum

$$d^2=l^2+b^2$$

Melody  May 28, 2017
#3
+90544
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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
+1221
+1

$$\sqrt{2l^2}=l\sqrt2$$

$$\sqrt{2l^2}$$

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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