SOLUTION: the area of a square is 144 square centimaters.find the length of the diagonal. write your answer in simplest radical form.

Algebra ->  Pythagorean-theorem -> SOLUTION: the area of a square is 144 square centimaters.find the length of the diagonal. write your answer in simplest radical form.      Log On


   



Question 1009603: the area of a square is 144 square centimaters.find the length of the diagonal. write your answer in simplest radical form.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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For a square:
area=side%5E2
144cm%5E2=side%5E2
12cm=side
The sides of the square are 12 cm.
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The diagonal is the hypotenuse of a isosceles
right triangle with the square's sides as legs:
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S=length of sides; D=length of diagonals
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S%5E2%2BS%5E2=D%5E2
2S%5E2=D%5E2
2%2812cm%29%5E2=D%5E2
2%28144cm%5E2%29=D%5E2
288cm%5E2=D%5E2
sqrt%28288cm%5E2%29=sqrt%28D%5E2%29
12sqrt%282%29cm=D