| It is possible to enclose the same amount of
area within objects that have different perimeters! It's
true.....here take a look:
 |
Area = 4
square inches
Perimeter = 8 inches |
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Area
= 4 square inches
Perimeter = 10 inches |
 |
Area = 4
square inches
Perimeter = 17 inches |
Let's play with this a bit.
- How many different ways can you make an area of 8
square inches using only whole inches for length and width?
When you think you know click HERE to check your answer.
...
- Which of the above dimensions gives the smallest
perimeter?
ANSWER
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- How many different ways can you make an area of 11 square inches using
only whole inches for length and width?
ANSWER
...
- How many different ways can you make an area of 12 square inches
using only whole inches for length and width?
ANSWER
...
- Which of the above dimensions gives the smallest perimeter?
ANSWER
...
- NOW..........What is going on here........Do you see a
pattern?...........The smallest perimeters are occurring when?
ANSWER
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- If I am allowed to use fractions or decimals, not just
whole numbers, can I get the perimeter even smaller on the 12 square inch
question?
Try it using your calculator.
ANSWER
...
- Draw a figure that has a very LARGE perimeter and a small area.
click HERE to see my solution (*infinite answers are possible here)
2 ways (1 x 8, 2 x 4)
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2 x 4
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1 way because 11 is prime; its only whole number factors
are 1 and itself. So the rectangle would be 1 x 11 inches.
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3 ways (1 x 12) , (2 x 6), (3 x 4)
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3 x 4 gives a perimeter of 14 inches,
all the other perimeters are larger.
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When the dimensions are closest together like 2 x 2,
2 x 4, 3 x 4
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Yes, it will get a bit smaller
I tried 3 1/2 x 3 3/7 = 12 this gives a perimeter of 13 6/7
or
13.857142...
I tried to get it in a bit smaller and used the square root of 12 rounded to the
nearest ten-thousandth, this gave: 3.4641 x 3.4641 = approx.12 and yields a perimeter of
approx.13.8564
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Here is my drawing. It is a pink lake. If you
walk around this lake, you cover a lot of distance, but actually there is very little room
to water ski!
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