SOLUTION: the area of a square is 81 square centimeters, find the length of the diagonal.

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Question 554914: the area of a square is 81 square centimeters, find the length of the diagonal.
Found 2 solutions by nyc_function, MathTherapy:
Answer by nyc_function(2741)   (Show Source): You can put this solution on YOUR website!
The area of a square = side times side.

In short, A = s times s or s^2

81 = s^2

Taking the square root of both sides, we get s = 9cm.

To find the diagonal, we use the Pathygorean Theorem.
Let d = the diagonal representing the hypotenuse of the right triangle formed by two sides of the square and the diagonal.

(side)^2 + (side)^2 = (diagonal)^2

9^2 + 9^2 = d^2

81 + 81 = d^2

162 = d^2

Taking the square root of both sides, we get d = sqrt{162}.

The length of the diagonal is the square root of 162
written as sqrt{162}.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

the area of a square is 81 square centimeters, find the length of the diagonal.

The diagonal of the square will form two 45-45 right triangles

In any 45-45 right triangle (isosceles right triangle), the hypotenuse equals one side, times square root of 2 (radical 2). Since one side = 9, then the length of the hypotenuse or the length of the diagonal can be written as:



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