find the length of a side of a square whose diagonal is 36 in.
s sqrt 2 = 36
s = 36/sqrt 2
To find the length of a side of a square when the diagonal is given, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length 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, all sides are equal in length, so we can let "s" represent the length of each side.
Using the Pythagorean theorem, we can set up the following equation:
s^2 + s^2 = 36^2
Simplifying the equation, we get:
2s^2 = 36^2
Dividing both sides by 2, we have:
s^2 = (36^2) / 2
Calculating the right side of the equation, we have:
s^2 = 1296 / 2
s^2 = 648
To solve for "s", we take the square root of both sides:
s = sqrt(648)
s ≈ 25.46 (rounded to two decimal places)
Therefore, the length of each side of the square is approximately 25.46 inches.