The diagonal of a square is formed by connecting the opposite corners with a straight line. Knowing the length of the diagonal will help you find dimensions of the two right triangles formed within the square. While you can measure a diagonal with a ruler, you can also use the Pythagorean theorem to find its length.
The Pythagorean Theorem
A square split in half diagonally forms two right triangles. Each of these triangles has two equal legs, or sides, that are the same length as the sides of the square. The hypotenuse, or side opposite the right angle, is identical to the diagonal of the square. Using this knowledge, you can find the length of the diagonal of the square with the Pythagorean theorem, which states that the sum of the squares of the two equal sides, a and b, is equal to the square of the hypotenuse, c: a^2 + b^2 = c^2. For example, you have a square with sides 5 inches long. Your equation reads 5^2 + 5^2 = c^2. After multiplying, you have 25 + 25 = c^2. Add to find 50 = c^2. Take the square root of both sides to find the diagonal is 7.07 inches.
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