Thread: help pleaseeeeeeeee

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.

Hello, doneng!

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: . .[1]

The area of the rectangle is: . .[2]

Substitute [1] into [2]: .

Differentiate and equate to zero: .

Substitute into [1]: .

Therefore, the maximum area is: .