Question 1171698
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x = side length of the square
Any square has all four sides the same length, so each side is x centimeters long.
It doesn't make sense to have x be negative, so we'll say x > 0.


Draw a square with one diagonal only. We have the square divided into two congruent right triangles. Focus on one of those right triangles.


This right triangle has congruent legs (x cm each) and a hypotenuse that is 10 cm long.
We'll let
a = x
b = x
c = 10
which will be plugged into the Pythagorean theorem to solve for x.


a^2 + b^2 = c^2
x^2 + x^2 = 10^2
2x^2 = 100
x^2 = 100/2
x^2 = 50
x = sqrt(50) .... applying the square root, keep in mind that x > 0
x = sqrt(25*2)
x = sqrt(25)*sqrt(2)
x = 5*sqrt(2)


Each leg is exactly 5*sqrt(2) cm long


Therefore, each side of the square is 5*sqrt(2) cm long.


This is known as the exact answer because we don't have any decimal approximations going on. 


Use of your calculator should lead to the rough approximation of
5*sqrt(2) = 7.0710678
Note that
sqrt(50) = 7.0710678
to help confirm that sqrt(50) = 5*sqrt(2)


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Exact Answer: 5*sqrt(2)   cm
Approximate Answer: 7.0710678  cm
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