help me answer this question:

A rectangle is inscribed in a right triangle of sides 6, 8 , 10 so that two of the sides are on the triangle. Find the rectangle of maximum area.


- the question has to do with maximum and minimum. i suppose this one is a maximum.

- first step is to write an equation for what you are trying to maximize/minimize. (drawing it may help as well)

- after that, take the derivative, make it equal to zero, take the partition number and make a sign chart out of it. find out if that partition number is a local maximum.

- take the number and answer the question.

should be easy, just having a hard time with the writing an equation part.

The rectangle is defined by the slope of the side of the triangle that is not parallel to either the y or x axes. This line can be written as y=-(3/4)x + 6.

The rectangle inside the triangle has side lengths of x and y, and y = the equation above. Therefore, area = x((-3/4)x + 6) which distributes to (-3/4)x^2 + 6x, for 0<x<8.

With the equation for area, now take the derivative, set it equal to zero and solve for x. X represents how far along the x axis the right side of the rectangle is, if the triangle has its 90 degree corner in the first quadrant.

never took calculus. algebra 3/trig is as far as i got, and alot of that i don't remember.

The rectangle is defined by the slope of the side of the triangle that is not parallel to either the y or x axes. This line can be written as y=-(3/4)x + 6.

The rectangle inside the triangle has side lengths of x and y, and y = the equation above. Therefore, area = x((-3/4)x + 6) which distributes to (-3/4)x^2 + 6x, for 0<x<8.

With the equation for area, now take the derivative, set it equal to zero and solve for x. X represents how far along the x axis the right side of the rectangle is, if the triangle has its 90 degree corner in the first quadrant.

you sumbitch. your a smart one :wiggle: .

thanks alot <3

Lol, Pugg57 got it too on the RXclub.

Took me a couple minutes to figure out how to approach it, and I had to make a sketch of the triangle / rectangle.

Glad I could help! :)

you sumbitch. your a smart one :wiggle: .

thanks alot <3

You're.

Learn English before math.

All hail the fuhrer of spelling!