Question 157456: FIND THE SIDE OF A SQUARE WHOSE DIAGONAL IS 5 CM
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! FIND THE SIDE OF A SQUARE WHOSE DIAGONAL IS 5 CM.
Let s = side of this square
The diagonal is our hypotenuse and any two sides can be the two legs.
We use the Pythagorean Theorem to find s.
s^2 + s^2 = 5^2
2s^2 = 25
Divide both sides by s.
s^2 = 25/2
Take the square root of both sides.
s = sqrt{25/2}
We can house the numerator and denominator into their own radical symbol.
s = sqrt{25}/sqrt{2}
s = 5/sqrt{2}
We rationalize the denominator because a radical is never accepted in the denominator.
Doing so, our final answer is:
side of this square = 5(sqrt{2})/2....This is read: "Five times the square root of two divided by two."
Is this clear?
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