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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