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What is the length of the side of a square whose diagonal is 10?

1 Answer

Answer:

Draw a diagram to represent your situation.

Explanation:

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Since we're dealing with a square, all side lengths measure the same thing. Furthermore, the angle B and D are right, therefore allowing us to use pythagorean theorem to find the value of a.

#color(blue)(a^2 + b^2 = c^2#

Where #aand b# are the right containing sides

Since #aandb# are equal,we consider them as #a#

#c# is the Hypotenuse of the right-triangle

The diagonal is the Hypotenuse #c#

#rarra^2 + a^2 = 10^2#

#rarr2a^2 = 100#

#rarra^2 = 50#

#rarra = sqrt(50)#

#color(green)(rArra=sqrt(25*2)=5sqrt2#

So, the side lengths measure #5sqrt(2) or 7.07# units each.

Hopefully this helps!