In a right triangle, the two legs measure 12 cm and 16 cm. A rectangle is inscribed within this triangle such that one side of the rectangle lies along the hypotenuse of the triangle, and the opposite vertices of the rectangle touch the legs of the triangle. What is the maximum area of the rectangle?
To determine the area of the rectangle, we need to find the length of its sides in relation to the triangle's dimensions. First, calculate the hypotenuse using the Pythagorean theorem, then apply the properties of similar triangles.