Katetuotteen

Katetuotteen is the product of the lengths of the two catheti (legs) of a right triangle. If the legs have lengths a and b, the katetuotteen equals ab. It enters directly into the area formula for a right triangle: A = 1/2 ab, so the katetuotteen is twice the area and is symmetric in the legs.

For a triangle with hypotenuse c and an acute angle α opposite leg a, we have a = c cos α and b = c sin α, giving katetuotteen ab = c^2 sin α cos α = (c^2/2) sin 2α. With fixed c, ab is maximized when α = 45°, yielding ab_max = c^2/2. Example: a right triangle with legs 3 and 4 has katetuotteen 12 and area 6.