Which is closest to the length of the diagonal of a square whose sides measure 20 cm?
The exact answer is 20 sqrt2. What are your choices?
28 cm
28 cm is correct.
To find the length of the diagonal 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 the case of a square, the two sides are equal in length, so we can denote the length of one side as "s." The diagonal of the square (d) is the hypotenuse of a right triangle formed by the two sides.
Using the Pythagorean theorem, we have:
d^2 = s^2 + s^2 = 2s^2
To find the length of the diagonal (d), we need to find the square root of the right-hand side of the equation. Let's substitute the given side length (s = 20 cm) into the equation and solve for d:
d = √(2s^2)
= √(2 * 20^2)
= √(2 * 400)
= √(800)
≈ 28.28 cm
Therefore, the length of the diagonal of a square with sides measuring 20 cm is approximately 28.28 cm.