# Homework Help: Problems involving maximum and minimum values

1. May 30, 2005

### imbecile

here comes the question

A varianble rectangle is inscribed in a given semicircle, so that one side lies along the bounding diameter, and two vertices lie on the bounding arc.
1 Show that wgeb tge area if tge rectangle is greatest, the sides of the rectangle are in the ratio 2:1

2 Show further that when the perimeter of the rectangle has a turning value the sides are in the ratio 4:1,
and determine the nature of the turning value.

Ans:maximum

:surprised :rofl: :yuck:

2. May 30, 2005

### whozum

Last edited by a moderator: Apr 21, 2017
3. May 30, 2005

### HallsofIvy

You have a rectangle inscribed in a semi-circle (radius not given so call it R). One side of the rectangle is along the diameter of the semi-circle. If we call the length and width of the rectangle l and w, then the area is lw and the perimeter is 2l+ 2w.
Now: can you write w (and therefore the area and perimeter) as a function of l only?
What is the derivative, with respect to l, of the area and perimeter functions?

4. Jun 5, 2005

### imbecile

whozum

excuse me whozum,
if i didn't try my best to figure out this question will i simply post it here??
i had read the that section the first day soon after i become a member here.
if i didn't put any effort on this questions will i put any extra effort to come here and type the question to post it up here????? i would rather ignore the question.
BTW, this is not my homework, this is the exercises i make myself do as i didn't go for math tuition or extra classes.

5. Jun 5, 2005

### imbecile

HallsoftIvy

okei
if u mention it that way,,,,,,,
can the rectangle be rectangle when inscribed in it with one side of the length is the diameter of the semicircle?
i tried to draw it before i post this question and i found that to be a shape like trapezium..?? :uhh:

Last edited: Jun 5, 2005
6. Jun 5, 2005

### HallsofIvy

Yes, that's what inscribed means!

??? What do you have to do to get a rectangle, rather than a trapezium? Is the side on the diameter of the semicircle symmetric with respect to the center of that line?