Function Problem: Area of Rectangle with 100ft Perimeter

  • Thread starter Thread starter Arreat
  • Start date Start date
  • Tags Tags
    Function
AI Thread Summary
To express the area of a rectangle with a perimeter of 100 feet as a function of the length L, the perimeter equation 100 = 2w + 2l can be rearranged to find width in terms of length. The correct area function is A(w) = w(50 - w), which simplifies to A = -w^2 + 50w. However, since the problem requires the area as a function of length, width must be expressed in terms of length using the perimeter equation. Substituting this into the area formula yields a function for area based on length.
Arreat
Messages
1
Reaction score
0

Homework Statement



Express the area of a rectangle with the perimeter of 100 feet as a function of the lengh L of one of its sides


Homework Equations


100=2w+2l


The Attempt at a Solution


As far as I can get is,

L = 50 -2w

Just writing the function is a problem, I assume it's something like but I'm not sure, sorry if I'm completely off it's been a long day.
A(W) = (50-2w)(w) = 50w - 2w^2
or
A = w(50-w)
 
Physics news on Phys.org
You successfully wrote the function for area (in two equivalent forms).
 
If 100=2L+2W

then L=50-W but L\neq 50-2W

Therefore your 2nd equation for the function is the correct one. A=-W^2+50W

But the question asked as a function of the length, not width. It will be similar though. Just make width the subject of the perimeter equation and substitute into the area formula.
 
Last edited:

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Finding the length and width of rectangle
Replies
8
Views
3K
Draw a rectangle that gives a visual representation of the problem
Replies
14
Views
2K
Minimum of x+1/x (Perimeter Square < Perim equal area rects)
Replies
1
Views
2K
Maximizing Area of Norman Window
Replies
1
Views
12K
MHB Find Perimeter of Rectangle with Given Area and Width
Replies
21
Views
3K
How do I express the area of a Norman window as a function of its width?
Replies
18
Views
6K
MHB Find Area Formula of Rectangle
Replies
2
Views
2K
Function expression, area of a window
Replies
29
Views
4K
Area of Norman Window: Function of Width x
Replies
19
Views
8K
What is the Domain of the Area Function for a Rectangle on a Parabola?
Replies
15
Views
4K

Hot Threads

Recent Insights

Back
Top