SOLUTION: How do you find the area and perimeter of a square when you are only given the diaganol length of 18meters? Thanks:]

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Question 551827: How do you find the area and perimeter of a square when you are only given the diaganol length of 18meters? Thanks:]
Found 2 solutions by jim_thompson5910, TutorDelphia:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: If the side length of the square is x, then 2x%5E2=d%5E2 where d is the diagonal. So because the diagonal is 18 m, we know that d = 18 and 2x%5E2=18%5E2


Once you have the side length, you can plug it into the formulas


Area: A=s%5E2


Perimeter: P=4s


where 's' is the side length

Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal length is the hypotenuse to a right triangle where the sides have equal length
From the Pythagorean theorem we know that
a%5E2%2Bb%5E2=c%5E2
Since the sides a and b are the same we can rewrite it as
s%5E2%2Bs%5E2=18%5E2
combine like terms
2s%5E2=324
divide both sides by 2
s%5E2=162
Since s%5E2 is my area formula for a square, 162 is my area.
The perimeter will be 4*s
take the square root of both sides
s=12.73m
4s=50.91