How to Measure Diagonals

Measure the diagonal of any right triangle given the values of its two other sides.

Being able to measure diagonals is important in mathematics because diagonals are commonplace lines that show up in right triangles and squares -- the latter of which are just collections of two right triangles. According to the Pythagorean Theorem, the diagonal of a right triangle (H) relates directly to the other lines (A and B) via an equation. And it's through this equation that you can measure the diagonal of any right triangle or square.

Instructions

1. Recognize the relationship between A, B and H, which according to the Pythagorean Theorem is A^2 + B^2 = H^2.

2. Plug the values of the sides into the equation. Given a right triangle with A and B values of 3 and 4, respectively, the equation would be 3^2 + 4^2 = H^2. Given a square with A and B values of 3 -- remember that a square has equal sides -- then the equation would be 3^2 + 3^2 = H^2, or 2(3^2) = H^2.

3. Solve the equation you obtained in step two to measure the diagonal. Given a right triangle with sides 3 and 4, for instance, the solved equation would read

   3^2 + 4^2 = H^2

   9 + 16 = H^2

   25 = H^2

   sqrt(25) = H

   5 = H

References

• Palm Beach State College: The Pythagorean Theorem