Squares on the Sides

Part of the Triangles section of Coddy's Geometry journey. Lesson 29 of 71.

Draw a square on each side of a right triangle with legs 3 and 4 and hypotenuse 5. The square on the leg 3 has area 9. The square on the leg 4 has area 16. The square on the hypotenuse has area 25. The two smaller areas add up to the largest one: 9 + 16 = 25. The same is true for every right triangle, whatever its size.

$A right triangle with legs 3 and 4 and hypotenuse 5, with a square drawn on each side, their areas 9, 16 and 25$

The two smaller squares fill the largest: 9 + 16 = 25

The Pythagorean theorem says that in a right triangle with legs a and b and hypotenuse c,

a^2 + b^2 = c^2

Square the two leg lengths and add them. The result is the square of the hypotenuse. The legs are the two sides that meet at the right angle. The hypotenuse is the side opposite the right angle. Find those three sides first, then put their lengths into a^2 + b^2 = c^2.