# The area of a square is 81 square centimeters. What is the length of the diagonal?

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The length of the diagonal of the square is approximately 12.73 centimeters.

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To find the length of the diagonal of a square, you can use the Pythagorean theorem. In a square, the diagonal forms a right triangle with the sides of the square.

Let ( s ) be the length of one side of the square. According to the Pythagorean theorem: [ \text{Diagonal}^2 = \text{Side}^2 + \text{Side}^2 ]

Given that the area of the square is 81 square centimeters, we can find the length of one side (( s )) using the formula for the area of a square: [ \text{Area} = \text{Side} \times \text{Side} ] [ 81 = s \times s ]

Solve for ( s ): [ s = \sqrt{81} = 9 ]

Now, substitute the value of ( s ) into the Pythagorean theorem: [ \text{Diagonal}^2 = 9^2 + 9^2 ] [ \text{Diagonal}^2 = 81 + 81 ] [ \text{Diagonal}^2 = 162 ]

Take the square root of both sides to find the length of the diagonal: [ \text{Diagonal} = \sqrt{162} \approx 12.73 \text{ centimeters} ]

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