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

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Question 948502: The diagonal of a square is 42.5 cm . Calculate the perimeter and the area of the square
Answer by macston(5194) About Me  (Show Source):
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The diagonal(d) of a square forms the hypotenuse of a right triangle with two of the sides as legs. Thus:
s%5E2%2Bs%5E2=d%5E2
2s%5E2=d%5E2 Find the square root of each side
sqrt%282%29%28s%29=d Divide each side by sqrt%282%29
s=d%2Fsqrt%282%29 Substitute value of diagonal
s=42.5cm%2Fsqrt%282%29
Area of a square=s%5E2
Area=%2842.5cm%2Fsqrt%282%29%29%5E2=%28%2842.5cm%29%5E2%29%2F2=1806.25 sq cm/2=903.125 sq cm
ANSWER 1: Area of the square is 903.125 sq cm.
Perimeter of a square=4s=4%2842.5cm%2Fsqrt%282%29%29=170cm%2Fsqrt%282%29=120.2 cm
ANSWER 2: Perimeter of the square is 120.2 cm.