Yes another math thread.(HOMEWORK HELP!)

I feel kinda weird asking for homework help on here but I've never done it before and I really need this grade. I asked my sister, my parents and they tried for awhile to figure it out, but they couldn't either. It's extra credit and I NEED it. So anyway the problem is:

Toni bought 36 feet of fence to make a pen for her dog, Spike. She wants to use all 36 feet.

a.) If she makes the pen rectangular, what are the dimensions of the pen with the largest area she can make?
b.) If she makes the pen circular would it have more or less area? Work Must be shown.
c.) If she uses her garage as one side of the pen, and she wants it to be rectangular, what are the dimensions of the pen that would give her the biggest area?


It's not sure until next week I think..but I want to hand it in early. Thanks! ;)

1. the largest area Tony can get is if the rectangular is a square. You know what the perimeter of the square is which is the total length of the fence so you can work out the dimension of the square.

2. the circumference of the circle is also the total length of the fence so you can work out the radius of the circle and from that work out the area of the circle. You can then compare the area of the square and the circle and see which has a bigger area.

3. same as 1, the biggest area is a square. the total length of the fence, however, equals three sides of the square because Tony is using the garage as one of the side. You can work out the side of the square and then calculate the area.

Good luck with your homework!

Can you get a piece of string, 36 inches long? The play around with that and see what you get.

I'm a whiz with number problems but i cant do dimension/word problems well.

Quote:

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Originally Posted by Maltese_Love

I feel kinda weird asking for homework help on here but I've never done it before and I really need this grade. I asked my sister, my parents and they tried for awhile to figure it out, but they couldn't either. It's extra credit and I NEED it. So anyway the problem is:

Toni bought 36 feet of fence to make a pen for her dog, Spike. She wants to use all 36 feet.

a.) If she makes the pen rectangular, what are the dimensions of the pen with the largest area she can make?
b.) If she makes the pen circular would it have more or less area? Work Must be shown.
c.) If she uses her garage as one side of the pen, and she wants it to be rectangular, what are the dimensions of the pen that would give her the biggest area?


It's not sure until next week I think..but I want to hand it in early. Thanks! ;)

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a. a rectangle has 4 sides. So, take the 36 feet and divide it by 4 sides. That means each side would be 9 feet long.

b. hmmmmmmm

c. If she uses the garage as one side of the pen, then she's using the 36 feet to build the other 3 sides. 36 divided by 3 = 12. Each of the 3 sides would be 12 feet.

I didnt do work on this problem but i used logic, so here goes:
b.) If she makes the pen circular would it have more or less area? Work Must be shown.
Less because of the fact that the squares around the edges of the circle would be divided in half.

b)
The area covered by the square 81 sq ft (=9 ft x 9 ft)

The rope is 36 ft long so if you put it in a circle the circumference of the circle is 36 ft.
The formula for the circumference is 2 pi x r (r as in radius)
2 pi times r = 36 ft
r = 36 ft / 2 pi

The area covered by a circle of radius r is pi times r exp 2. When the radius is 36 ft/ 2 pi, then pi times r exp 2 is pi *36 ft * 36 ft / (2pi *2 pi) = 36 * 36 sq ft/ 4 pi = 36*9/pi = 324/3,14 = ca. 103

So the circle will cover a bigger area.

Reggie- the radius of the circle is bigger than half the side of the suare, so while the corners of the square will lie outside the circle, the circle lies outside the corners more by the sides (I wish I could draw it).

Quote:

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Originally Posted by vinjashira

1. the largest area Tony can get is if the rectangular is a square. You know what the perimeter of the square is which is the total length of the fence so you can work out the dimension of the square.

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The perimeter = 36 ft.
Each side of the square = 36 : 4 = 9 ft.
Area of the square = 9 x 9 = 81 sq ft.

(The square gives the largest are - because if Tony do not make a square, but instead he'll make a rectangula side 10 ft x 8 ft. Total area is only 80 sf)

Quote:

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Originally Posted by vinjashira

2. the circumference of the circle is also the total length of the fence so you can work out the radius of the circle and from that work out the area of the circle. You can then compare the area of the square and the circle and see which has a bigger area.

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First lets remember that for a circle, the Circumference = Pi x Diameter (d)
36 ft = 3.14 x d
d= 36 : 3.14 = 11.46 ft.

Now, Diameter = 2 x Radius (r)
11.46 = 2 x r
r= 11.46 : 2 = 5.73 ft.

Area = Pi x r2 = Pi x r x r = 3.14 x 5.73 x 5.73 = 103.10 sq ft.

Since the area of the square is 81 sf, and area of the cicle is 103.10 sf. The area of the circle is larger.

Quote:

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Originally Posted by vinjashira

3. same as 1, the biggest area is a square. the total length of the fence, however, equals three sides of the square because Tony is using the garage as one of the side. You can work out the side of the square and then calculate the area.

Good luck with your homework!

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Each side of the square is 36:3 = 12 ft.
Total area = 12 x 12 = 144 sq ft.

Vinjashira, you're excellent at math :D

Thanks alot guys! =) I really appreciate it. I will hand it in tomorrow and see what I get for extra credit. It's worth 15 points. I'll tell you what I get. :)

Holy cow! THAT is only worth 15 points?! I hope you understood those explanations, cause a few of them had my head spinning (another reason I'm a librarian, NOT a math teacher!).

I'm helping an 8th grader with Algebra 1, and thank goodness Prentice Hall(the publisher of the math book) has an online guide and tutoring video manual. It's amazing how much you forget when you don't use it!