SOLUTION: The diagonal of a square is 42.5 cm. Calculate the perimetre and area of the square.

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Question 204918: The diagonal of a square is 42.5 cm. Calculate the perimetre and area of the square.
Found 2 solutions by nerdybill, alicealc:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of a square is 42.5 cm. Calculate the perimetre and area of the square.
.
Let x = length of one side of the square
then from Pythagorean theorem we have:
x^2 + x^2 = 42.5^2
2x^2 = 1806.25
x^2 = 903.125
x = 30.052
.
Perimeter = 4x = 120.208 cm
Area = x^2 = 903.125 sq cm

Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
diagonal of a square with the side x is x%2Asqrt%282%29
x%2Asqrt%282%29=42.5
x=42.5%2Fsqrt%282%29

perimeter = 4x
= 4%2A42.5%2Fsqrt%282%29+=+170%2Fsqrt%282%29
= %28170%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29
= %28170%2Asqrt%282%29%29%2F2
= 85%2Asqrt%282%29+cm

area = x%5E2
= %2842.5%2Fsqrt%282%29%29%5E2
= 1806.25%2F2
= 903.125 cm^2