A square is cut on the diagonal to form two right triangles the hypotenuse of the resulting triangles is 20 inches long what is the length of each of the sides
Let's assume the length of one side of the square is "s" inches.
Since the square is cut along the diagonal, the hypotenuse of each right triangle formed will be the length of the diagonal of the square, which is given as 20 inches.
In a right triangle, the hypotenuse (c) is related to the other two sides (a and b) by the Pythagorean theorem:
c^2 = a^2 + b^2
Since the triangles are right triangles and the diagonal is the hypotenuse, the sides of each triangle will have the same length.
So for each triangle, we have:
c = 20 inches
a = b = s (since they have the same length)
Now we can substitute these values into the Pythagorean theorem equation:
20^2 = s^2 + s^2
400 = 2s^2
Divide both sides of the equation by 2:
200 = s^2
Take the square root of both sides to find the value of "s":
√200 ≈ 14.14
Therefore, the length of each side of the square is approximately 14.14 inches.