a rectangle is to be inscribed in a right triangle having sides of lengty 6 in, 8 in, and 10 in. find the dimension of the rectangle with greatest area..(Thinking)

tq~

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- Mar 3rd 2010, 11:18 PMredcherrythis is applied maximum and minimum problems
a rectangle is to be inscribed in a right triangle having sides of lengty 6 in, 8 in, and 10 in. find the dimension of the rectangle with greatest area..(Thinking)

tq~ - Mar 4th 2010, 03:41 AMArchie Meade
Hi redcherry,

If you draw the right-triangle, with an arbitrary inscribed rectangle,

that has sides against the base and vertical side, settling in the

right-angled corner.

label the base of the triangle 6, height 8, hypotenuse 10.

The rectangle base is x and the rectangle height y.

Now, observe the smaller identical triangle at the bottom corner.

It has base (6-x) and height y.

Hence we can write an equation

Rectangle area is

in terms of x only, allowing us to differentiate the area and equate the derivative to zero to find the rectangle of maximum area

which equals zero when x=3