Posted by **math** on Monday, October 26, 2009 at 6:26pm.

What is the area of the largest rectangle that can be placed in a 5-12-13 right triangle (as shown)?

- Calculus -
**MathMate**, Monday, October 26, 2009 at 7:32pm
Let ABC be the vertices of the triangle, right-angled at B, AB=5, BC=12 (vertical side), AC=13.

Draw a rectangle BDEF, where D is on AB, E is on AC and F is on BC.

Denote

x=DE= height of rectangle

Width of rectangle = DB = 5-(5x/12)

Area of rectangle,

A(x)=x(5-(5x/12))=5x-5x²/12

A'(x) = 5-10x/12

For A(x) to be maximum,

A'(x) = 0 = 5-10x/12

x=6, 5-5(6)/12 = 2.5

The maximum area is 6*2.5=15

Note that the aspect ratio of the rectangle is the same as that of the right sides of the triangle.

## Answer this Question

## Related Questions

- Calculus - 3) Consider rectangles located as shown in the first quadrant and ...
- CALCULUS - Find the area A of the largest rectangle that can be inscribed in a ...
- calculus - A rectangle is to be inscribed in a right triangle having sides of ...
- 5th grade - For each right triangle, draw the rectangle made by drawing sides ...
- geometry - The height of triangle ACE is 12 and base AE=20. A rectangle is ...
- Math - In the figure below, the diagonal line divides the rectangle into halves ...
- Math - The first question is this: Helen designs a rectangle with an area of 225...
- Calculus - Hello, could someone please help me with this problem? I'm a little ...
- algebra 1 - Evan is making a table that will be created in the shape of the ...
- calculus - find the area of the largest rectangle having one side on the x axis ...

More Related Questions