# Algebra

posted by .

Building windows: Window World, Inc., is responsible for designing new windows for the expansion of the campus chapel. The current design is shown in the figure. The metal trim used to secure the perimeter of the frame is 126″ long. If the maximum window area is desired (to let in the most sunlight), what will be (a) the dimensions of the rectangular portion of each window? (b) the total area of each window

• Algebra -

no figure, but from the context it appears to be a rectangle and something else. Since it's a church, and the same kind of problem has appeared here before, I assume the top portion is a semi-circle.

So, with width w and height h, the perimeter is w+2h+pi*w/2. The trim is not used between the top and bottom portions of the window.

So, we have

w+2h+pi*w/2 = 126
so,
h = 63 - (pi+2)w/4

window area is rectangle + half-circle

a = wh + pi/8 w^2
= w(63 - (pi+2)w/4) + pi/8 w^2
= 63w - pi/8 (2pi+3)w^2

da/dw = 63 - pi/4 (2pi+3)w
max/min area is where da/dw = 0

w = 252/(3pi + 2pi^2) = 8.64

Now you can figure the areas.

## Similar Questions

1. ### computer

What is the chronological order of the release of Microsoft GUI operating system?
2. ### computer

In Windows Vista, which button is used to create a new folder?
3. ### math

The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?
4. ### math (Ms.Sue)

your room has 2 windows.Each window occupies 11.76 square ft of wall space.if the windows are each 2.8 ft wide,how tall is each window?
5. ### Algebra

Window World, Inc. is responsible for designing windows for the expansion of the campus chapel. The current design is shown in the figure. The metal trim used to secure the perimeter of the frame is 126 inches long. If the maximum …
6. ### math

Diana designs stained-glass windows. She has a large supply of square glass window panes. Some panes are yellow, and some panes are red. She wants to place them in windows that are 3x2 in such a way that no two windows are the same, …
7. ### Math HELP!! :(

a contractor's designing one side of an office building 48 feet in length the windows are each 5 feet long and will be placed Six feet apart and 5 feet from the end of the building wall how many windows can a contractor design
8. ### Math

a contractor's designing one side of an office building 48 feet in length the windows are each 5 feet long and will be placed Six feet apart and 5 feet from the end of the building wall how many windows can a contractor design
9. ### Math

Please help Ms.Sue! a contractor's designing one side of an office building 48 feet in length the windows are each 5 feet long and will be placed Six feet apart and 5 feet from the end of the building wall how many windows can a contractor …
10. ### Introduction to Computers

The command prompt found on Windows 7 and Windows 8 is very similar to the interface of what past operating system?

More Similar Questions

Post a New Question