# Math Help - Quadratic Optimization

Hey, everyone! I've been working on my homework and this one problem's got me confused. Can someone help me get started? (Sorry, I'm rather lousy at math.)

A rectangle is bounded by the x-axis and the y-axis with a vertex on line p as shown below.

a) Write a formula for the base of the rectangle in terms of x.
b) Write a formula for the height of the rectangle in terms of x.
(Hint: find the equation of line p.)
c) Write a function for the area of the rectangle as a function of x.
d) What bae and height should the rectangle have in order to produce the rectangle with the maximum area? Find its area.

Really, I just need help setting up a and b. But any and all help is greatly appreciated!

2. Originally Posted by miyosuke
Hey, everyone! I've been working on my homework and this one problem's got me confused. Can someone help me get started? (Sorry, I'm rather lousy at math.)

A rectangle is bounded by the x-axis and the y-axis with a vertex on line p as shown below.

a) Write a formula for the base of the rectangle in terms of x.
b) Write a formula for the height of the rectangle in terms of x. (Hint: find the equation of line p.)
c) Write a function for the area of the rectangle as a function of x.
d) What bae and height should the rectangle have in order to produce the rectangle with the maximum area? Find its area.

Really, I just need help setting up a and b. But any and all help is greatly appreciated!
a) Base of the rectangle = x, where x is $0 \leq x \leq 40$
b) Height of the rectangle:
equation of the line is given by y = mx + b $\implies y = -\frac{1}{2}x + 20$

so ht of the rectangle is = $-\frac{1}{2}x + 20$, where $0 \leq x \leq 40$

3. Thanks kalagota, I managed to figure it out with your help. (Salamat, ha! )

4. Originally Posted by miyosuke
Thanks kalagota, I managed to figure it out with your help. (Salamat, ha! )
ui!! pinoy blood?

5. Originally Posted by kalagota
ui!! pinoy blood?
Hey! I've got some pinoy blood in my refrigerator. It makes really good beef stock.

-Dan

6. Originally Posted by kalagota
ui!! pinoy blood?
Opo.

Topsquark: Eep!

7. Originally Posted by miyosuke
Opo.

Topsquark: Eep!
naka-base ka sa US? wow!!