A square sheet of paper measures35 centimeters on each side. What is the length of the diagonal of this paper?

35^2 + 35^2 = d^2

1,225 + 1,225 = d^2

2,450 = d^2

_______ cm = d

Ah, the philosophical question of diagonals and squares! Well, my friend, to find the length of the diagonal of a square, we can turn to the Pythagorean theorem for help. If we let "a" and "b" be the length of the two sides of the square, and "c" be the length of the diagonal, then we have a classic case of a right-angled triangle. Using the theorem, which states that c² = a² + b², we can deduce that the length of the diagonal is quite simply the square root of two times the length of the side. So in this case, with a square sheet 35 centimeters on each side, the length of the diagonal is approximately 49.497 centimeters. That's one diagonal that won't be doing any sneaking around!

To find the length of the diagonal of a square, we can use the Pythagorean Theorem.

The Pythagorean Theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the sides of the square paper form a right triangle, with the diagonal being the hypotenuse.

So, let's calculate the length of the diagonal (D) using the Pythagorean Theorem:

D^2 = (35 cm)^2 + (35 cm)^2

D^2 = 1225 cm^2 + 1225 cm^2

D^2 = 2450 cm^2

Taking the square root of both sides to solve for D:

D = √2450 cm

D ≈ 49.5 cm

Therefore, the length of the diagonal of the square paper is approximately 49.5 centimeters.

To find the length of the diagonal of the square sheet of paper, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.

In a square, the sides are equal in length, so we can consider the sides as the two legs of a right triangle.

Let's denote the length of each side as "s" and the length of the diagonal as "d".

So, in this case, s = 35 centimeters. We need to find the length of the diagonal, which is d.

Applying the Pythagorean theorem, we have:

d² = s² + s²

d² = 35² + 35²

d² = 1225 + 1225

d² = 2450

To solve for d, we just need to take the square root of both sides:

d = √2450

Using a calculator or performing the calculations, we find that the length of the diagonal of the square sheet of paper is approximately 49.50 centimeters.