Find the area of the largest rectangle that can be inscribed in a right triangle
with legs of lengths 7 cm and 8 cm if two sides of the rectangle lie along the legs.Code:| 7 * | * | * | * P(x,y) o - - - - - o | | * | y| * | | * - - o - - - - - o - - - - - * - - | x 8
The equation of the hypotenuse is: . .
The area of the rectangle is: . .
Substitute  into : .
Differentiate and equate to zero: .
Substitute into : .
Therefore, the maximum area is: .