How to Figure the Length of the Diagonal in a Square

The two diagonals of a square are always congruent. In mathematical terms, the diagonal of a square is known as the hypotenuse of the two right triangles it creates. The Pythagorean theorem describes the relationship between the sides of the square and its hypotenuse; the square of the hypotenuse is equal to the sum of the squares of the two sides. From this theorem, you can compute the diagonal of the square given one of its sides.

Things You'll Need

• Calculator

Instructions

1. Get the measurement of the side of the square. Because the sides of a square are all equal, you need to know the measurement of just one side.

2. Calculate the square of the measurement.

3. Multiply the result by two. Because both sides are equal, you simply have to multiply by two the square of one side. For example, if "a" is the side of the square, using Pythagorean theorem, the square of the hypotenuse is equal to a^2 + a^2, which is simply 2a^2.

4. Get the square root of the product. For example, if you call the hypotenuse "h," h^2 = 2a^2. To get h, you must find the square root of both sides of the equality.

   Following the Pythagorean theorem, the computation for finding the hypotenuse of a square is:

   h^2 = 2a^2

   h = √(2a^2)

   h = a√2

   Finding the length of a diagonal given the side of a square, you multiply the length of one side by the square root of two.

References

• Math Open Reference: Diagonals of a Square
• Centre for Innovation in Mathematics Teaching: Unit 3 Section 2 : Calculating the Hypotenuse