How to Measure the Length of the Diagonal Line of a Square

A square's diagonal measurement is the same as the hypotenuse of its right triangles.
••• marekuliasz/iStock/Getty Images

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.

Related Articles

How to Find the Height of a Square
How to Find the Perimeter of a Right Triangle
How to Find the Missing Side of a Right Triangle
How to Solve a Hexagon
How to Find the Area & Width of a Rectangle
How to Find Dimensions in Geometric Shapes
How to Find the Area of a Shaded Part of a Square With...
How to Find the Area of Triangles & Trapezoids
How to Calculate Area of a Triangle
Characteristics of Aquatic Plants
How to Calculate Sides of a Triangle
How to Calculate Volume of a Circular Cylinder
How to Convert Square Dimensions to Round
How to Calculate the Square Feet on a Cube
How to Find the Slope of Linear Equations
How to Find the Height of a Rectangular Pyramid
How to Calculate the Area of a Curved Surface
How to Find the Height of a Square
How to Find a Parallel Line
How to Calculate Diagonal Distance Between Corners...

Dont Go!

We Have More Great Sciencing Articles!