The figure shows four squares. The smaller ones have side lengths a, b, and c. The vertices a and c of two of the smaller squares coincide with two diagonally opposite vertices of the large square. Vertex b of the third small square is on the side of the large one, which for the following expressions represents the side length of the largest square. Note that the two shaded triangles in the figure below are congruent as they have the same angle measures and the same hypotenuses. Then we can simply use the Pythagorean theorem to solve for x. Then we find that x equals the square root the quantity of a plus b squared plus c squared.

geometry

squares

Pythagorean theorem

congruent triangles

side length