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

Answer 1
If you note that #81# is a perfect square, you can say that for a real square shape:
#sqrt(81) = 9#
Furthermore, since you have a square, the diagonal, which forms a hypotenuse, creates a #45^@-45^@-90^@# triangle.
So, we would expect the hypotenuse to be #9sqrt2# since the general relationship for this special type of triangle is:
Let's show that #c = 9sqrt2# using the Pythagorean Theorem.
#c = sqrt(a^2 + b^2)#
#= sqrt(9^2 + 9^2)#
#= sqrt(81 + 81)#
#= sqrt(2*81)#
#= color(blue)(9sqrt2 " cm"#
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Answer 2

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

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Answer 3

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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