Miss Guy has a very energetic puppy. The puppy loves to play outdoors, so Miss Guy decided to build a pen to allow her pet to be outside while she is at school. She just happens to have 50 feet of fencing in her basement that she can use for the pen.
What are some of the ways she can set up the pen that uses all the fencing?
What are the dimensions of the rectangular pen with the most space available for the puppy to play?
Make sure you communicate ALL your work and thinking to receive credit!
33 comments:
She can set up the pen by 15 for the width and 10 feet for the length. I got this answer by just making sure that the total amount of feet matches the width and the height combined. She can also do 20 for the width and 5 for the length. 15 by 10 will give you the most space for the puppy to play.
All you have to do is make a polygon and if you add up all the sides you get EXACTLY 50.So you could do a pentagon with 10 feet on each side. Or you could do a decagon with 5 feet on each side.
Probably the pentagon with 10 feet on each side.
1. She can make a pentagonal shape with 10 ft on each congruent side.
2. She can do a fence design that has 10 sides and 5 ft on each side.
Those are the only two.
Miss. Guy can have each of the sides of the pen be 10 feet in length, (A decagon) or another way is with each side 5 feet in length. (A pentagon) (Those two ways are when all sides of the shape are equal.)
The dimensions of the rectangular pen with the most space available for the puppy is 12 feet in equal length on all sides of the rectangle.
First I wrote down the number 50 to know that that was the amount of fencing that Miss. Guy had. Then I divided to find out the all of the dimensions that could work for the puppy's pen.
she can have 10-ft sides(5x10=50) or she can have 15-ft parallel sides, and 10-ft bases.
Some ways you could use the fencing are ...
You could make the length 15 square feet and the width 10 square feet. Since 15+15=30 and 10+10=20 you can add 30+20 and get 50. 15x10=150 square feet which is your area.
You could also have the length 24 square feet and the width 1 square foot. Since 24+24=48, and 1+1=2 you can add 48+2 and get 50 square feet. 24x1=24 square feet which is your area.
You could also have the length 18 square feet and the width 7 square feet. Since 18+18=36, and 7+7=14, you can add 36+14 and get 50 square feet. 18x7=126 square feet which is your area.
The most room you could get is to make the length 13 square feet and the width 12 square feet. I knew to make the area the largest I would have to make the numbers close because the 2 University of Houston people taught us that when they gave us a lesson. Since 13+13=26 and 12+12=24 you can add 26+24 and get 50 square feet. 13x12=156 square feet which is the area.
First i did 10 x 5 and got 50 so he can have a 10 by 5 pen.....He can also have a 2 by 25 and i did 2 x 25 to get that answer....so my answer is 10 by 5 gives the puppy the most room to play...
My answer is a rectangular prism with length is 17ft, width is 17ft, and height is 16ft.
How I got my answer was by dividing the number of ft she had of fencing materials. '50 ft' by 3I divided the number of fencing by 3 because I needed to divide 50ft by length, width, and height and wanted to be almost equal .
My division: 50ft divided by 3 = 16ft remainder 2 ft of fencing.
Then I took the remainder from the division problem and divided it by 2 and got 1 to add to the length and width . so then the dog has more flooring to run on. That is how I got my answer.
Some ways are she can set up her puppy's pen is
I know:
that we only have 50 FT. of fencing!
she made a rectangular pen
MY ANSWER IS 10x15 THAT IS HOW I WOULD MWKE THE MOST SPACE AVAILABLE
One possible way that Miss Guy could set up her fence was that she could have 13ft on the opposite sides of the rectangle and 12ft on the other opposite sides.
This is how I got the answer:
I divided 50ft by 4 and got 12 remainder 2. I just added the 1 for two sides and that was 13ft on the opposite sides and 12 on the other opposite side.
I made an excel chart to communicate side lengths (Note:I sent you the chart).
The dimensions are a square of 12.5 feet times 12.5 feet for a total square footage of 156.25 square feet. (Note: I know how to multiply decimals.) If you want a regular answer, it is 13 feet by 12 feet for 156 square feet of space.
Miss Guy could make many pins for her puppy
*She could divide the 50 feet into 5 strips of 10 feet, this makes a pentagonal pin.
*Or she could divide the fencing into 10 strips of 5 feet, this makes a decagonal pin.
To find this answer I used my division facts and geometry to try to find a pin that would use all of the fencing.
1x24, 2x23, 3x22,ect. I know this because as long as the two numbers add up to 25 (excluding 0)I know that because 25+25=50, which is what the perimeter has to be. The answer to the second question is 12x13 or 13x12 because the closer 2 numbers you multipy are, the higher they usually will be. I need to multiply because the formula for area is length x width
I did 12.5ft. for each side, then divide it.
50/4=12.5
She can just use 12.5ft for each side.
The dimension is 12.5x4=50
The answer 13x12.because dimensions is Width times Length so we have to do 50 divide by 4 .then you get the answer.so the answer is 13x12.
A square is the biggest shape that can be used and you divide fifty by four to get the length of each side which is 12 and a half feet
I made a table to show the length/ width(it is a rectangle so the opposite sides are congruent) if the pen. There are 12 different ways she could have build te pen.
She could have:
# length width 1. 1 ft. by 24 ft. 2. 2 ft. by 23 ft. 3. 3 ft. by 22 ft.
4. 4 ft. by 21 ft. 5. 5 ft. by 20 ft. 6. 6 ft. by 19 ft. 7. 7 ft. by 18 ft. 8. 8 ft. by 17 ft. 9. 9 ft. by 16 ft. 10. 10 ft. by 15 ft. 11. 11 ft. by 14 ft. 12. 12 ft. by 13 ft. (and then, the length turns into width and the width turns into length)
Then to find the biggest pen (area) I made another table that looks alike but now, I have areas for each of them.
Areas of pen:
# length width area 1. 1 ft. by 24 ft. 23 sq.ft.
2. 2 ft. by 23 ft. 46 sq.ft.
3. 3 ft. by 22 ft. 66 sq.ft.
4. 4 ft. by 21 ft. 84 sq.ft.
5. 5 ft. by 20 ft. 100 sq.ft.
6. 6 ft. by 19 ft. 114 sq.ft.
7. 7 ft. by 18 ft. 126 sq.ft.
8. 8 ft. by 17 ft. 136 sq.ft.
9. 9 ft. by 16 ft. 144 sq.ft.
10. 10 ft. by 15 ft. 150 sq.ft.
11. 11 ft. by 14 ft. 154 sq.ft.
12. 12 ft. by 13 ft. 156 sq.ft.
So the dementions of the pen would be 12 ft. and 13 ft.
What I did was I drew a picture of the fenceing and I put 2 10's on paralle sides and I put 2 20's on paralle sides as well, and I think that that is the most room for the dog to play and run around in.
Two sides are both 15' long and the other two sides are 10' long each.
15+15+10+10=50'of fencing.
She has 50 feet of fencing
She could have 15 and 15 and 10 and 10
She could have 20 and 20 and 05 and 05
She could have 08 and 08 and 17 and 17
The biggest is probably :
15,15,10,and 10
triangle can be one 20ft.;20ft.; & 10ft. Another triangle that has
30ft.;10ft.; & 10ft.
20ft.; 20ft.; 5ft.; and 5ft. and another rectangle is 15ft.; 15ft.; 10ft.; and 10ft.All the fencing was used in all the tipes of ways to build the fence.
two ways you can do that are 20 by 5 or 15 by 10 if it is 20 by 5 he only gets 100 sq. feet to play on so 15 by 10 would make 150 sq. feet.
Answer - rectanegl/ square
Explanation - for a rectangel the sides are 15 ft(up and down)and there is 10 ft(sides)in the rectangel.So how you would come up with this is ..... 15+15+10+10=50.
first I drew a rectangle and labeled the sides.
Here are some ways:
15ft for the long side 10ft for short side.
16ft for long and 9ft for the short side.
20ft for the long and 5 for the short.
24ft for long and 2ft for short.
The dimension with the most space was 15 ft and 10 ft. I did area I did 15ft times 10ft = 150ft
First I thought in my head a picture of a fence 4 sides. i figured out that 2 sides could be 15 ft. and the other 2 could be 10. 15+ 15= 30 and 10+10=20 20+30=50
Well, here are 2 ways you can divide the 50ft. of fencing. 1) you can do one thats completely a rectangle. It is 20ft. by 5ft. but that does not provide the most space for the puupy. 2) the way that would give the puppy the most space would be a shape that is half square, half rectangle with a perimiter of 12 1/2 by 12.
To answer the second question is #2- 12 1/2 by 12.
(mathimatical thinking)
12 x 2 = 24 . 24+(12x2)=48 +1(2halfs)=50
50 ft. of fencing.
50/4 because to make a square pen.
12
4/50 R2
4v
10
8
2
12 R2
12 each side of the pen.
Then the rectangular pen is a 6x18 pen.
some of the dimensions are 13 by 12, 10 by 15, 18 by 7, 1 by 50 or 10 by 5. The most "roomy" area would be the 13 by 12 area fencing
One way she can set it up is a triangle one side is 20 ft. of fencing another side is 20 ft. of fencing and the last side is 10 ft. another shape can be a pentagon. Each side is 10 ft. long and there are 5 sides. The demensions for the rectangular pen are 2 ten ft. sides and 2 15 ft. sides.
She could set up a square with 12.5ft of fence on each side. Or she could set up a rectangle with 7ft on the long side, and 5.5ft on the short side. I think the square with 12.5ft on each side prevides the most room.
She could set up the pen and have 12 by 13 rectangle and have none left over. That would be the one with the most room for it. She could also do a 6 by 19, but that would not leave very much space. The least space would be 1 by 50, and it could run laps, but not much space for it to play!!
The type of pen that gave the uppy the most space is the 13 by 12. I got that answer by figuring out what numbers are closest that you you add 2 times each and get 50. The same dimensions are 12 by 13 if you want the most space availeble.
On 2 sides she can put up 15ft of fenceing.
On the other 2 sides she can put 10 ft of fenceing.
that would make a total of 50ft.
Post a Comment