SOLUTION: If a diagonal of a square is 18 cm, how long is a side?

Question 212404: If a diagonal of a square is 18 cm, how long is a side?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
pythagorean theorem states that a^2 + b^2 = c^2
let d = diagonal of the square.
let s = each side of the square.
diagonal is hypotenuse of a right triangle, so c = d
one side of the square is one leg of the right triangle so a = s
one side of the square is the other leg of the right triangle so b = s
a^2 + b^2 = c^2 becomes:
s^2 + s^2 = d^2 which becomes:
2s^2 = d^2
divide both sides by 2 to get:
s^2 = d^2/2
take the square root of both sides to get:
s = +/- sqrt (d^2/2)
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since s can't be negative, this becomes:
s = sqrt (d^2/2)
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since d = 18, this becomes:
s = sqrt(18^2/2) which becomes:
s = sqrt (162) which becomes:
s = 12.72792206
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2s^2 = 324
sqrt(324) = 18
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answer is confirmed.
each side of the square = 12.72792206
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