The area of a square is 81 square centimeters. What is the length of the diagonals?
9 is side
sqrt (9^2 + 9^2)
= 9 sqrt 2
To find the length of the diagonals of a square, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the diagonals form right angles with each side. Let's assume that the length of one side of the square is "s" centimeters. Since all sides of a square are equal, all four sides have the same length s.
To find the length of the diagonal, we will need to find the length of the sides first.
Given that the area of the square is 81 square centimeters, we can set up the equation:
Area = Side^2
81 = s^2
To solve for s, we take the square root of both sides:
√81 = √s^2
9 = s
So, the length of each side of the square is 9 centimeters.
Now, to find the length of the diagonals, we need to use the Pythagorean theorem.
In a right triangle formed by the diagonal and two sides of the square, one side is the length of a side of the square (9 cm), the other side is the length of a side of the square (9 cm), and the hypotenuse is the length of the diagonal (let's call it "d" centimeters).
Using the Pythagorean theorem, we have:
d^2 = 9^2 + 9^2
d^2 = 81 + 81
d^2 = 162
Taking the square root of both sides, we find:
d = √162
d ≈ 12.73
Therefore, the length of the diagonals of the square is approximately 12.73 centimeters.