Posted by **Anonymous** on Wednesday, December 5, 2007 at 11:59am.

Find the area A of the largest rectangle that can be inscribed in a right triangle withh legs of length 3cm and 4cm if two sides of the rectangle lie along the two legs of the triangle.

- CALCULUS -
**drwls**, Wednesday, December 5, 2007 at 9:09pm
Place the right angle at the origin and let the 3 cm length be along the x axis and the 4 cm length along the y axis.

Let x be the distance of one corner from the origin along the x axis.

The hypotenuse has the equation

y = 4 - (4/3)x

For the rectangle thus formed,

A = x*y = 4x - (4/3)x^2

This has a maximum when

dA/dx = 4 - (8/3) x = 0

x = (3/8)*4 = 1.5

y = 4 - (4/3)(3/2) = 2

A = 3 cm^2

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