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.

Results 1 to 2 of 2

- November 23rd 2008, 07:32 PM #1

- Joined
- Nov 2008
- Posts
- 6

- November 23rd 2008, 09:08 PM #2

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,941
- Thanks
- 798

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: .