Answer:
7.07 cm
Step by step explanation:
Let's use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In a square, the diagonals are the longest sides and they are equal in length. Let x be the length of one of the sides of the square, then we can use the Pythagorean theorem to find x:
(diagonal)^2 = (side)^2 + (side)^2
10^2 = x^2 + x^2 (since the diagonal is the hypotenuse of a right triangle formed by the two sides of the square)
100 = 2x^2
x^2 = 50
x = sqrt(50) = 5 * sqrt(2)
Therefore, the length of an edge of the square is 5 * sqrt(2) cm (approximately 7.07 cm to two decimal places).