The Fencing Problem
There is a need to make a fence that is 1000m long. The area inside
the fence has to have the maximum area. I am investigating which shape
would give this.
Triangles: Scalene
[IMAGE]
The diagram above is not to scale. Instead of having the perimeter to
1000m, only in this diagram, I have made the perimeters of the shape
to 10, only to make this part of the investigation easier to
understand. We know that the base of all the shapes is 2. The lengths
for the equilateral triangle are 4 on each side. This part of the
investigation is to explain why the triangle with the longest height
cannot have the same base. The tallest triangle also has a perimeter
of 10. One of the sides for the tallest triangle is 5, which is
understandable. However the other side is 3. This is literally
impossible to be because if this triangle was drawn to scale, then the
side that is 3 will not end up reaching the base. The isosceles
triangle has a side of 4 and it looks shorter than the side of 3. The
only way the higher triangle will reach is if the base is shortened.
So in the formula 'h x b ÷ 2', in the case of the higher triangle, the
height will be longer but the base will be shorter.
Looking at this diagram, there is no need to draw out tables to find
out whether or not a scalene triangle is bigger than an equilateral or
an isosceles in terms of area. I have made it so that the base is the
same width for all triangles. The lines that are going from top to
bottom on each triangle represent the height. It shows that if the
base stays the same for all triangles, a scalene can never have the
larger height and larger base than the isosceles and if it doesn't
have the larger height and base then it cannot have the larger area
either.
[IMAGE]
This shows that there is a difference of 2cm between A and B, and B
a level area of land. She is not concerned about the shape of the plot
“When I consider the nature of the triangle, it appears very clearly to me… that its three angles equal two right angles, and I cannot help believing this to be true as long as I attend to the proof; but as soon as I turn my mental gaze elsewhere, even though I may remember that I perceived it clearly, I can easily dou...
Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, isosceles triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and Fig 1. Table 1 showing the areas for the different shapes formed by using the
If I am to use a square of side length 10cm, then I can calculate the
In the play Fences written by August Wilson, Bono, an African American man living in the 1950s states that, “Some people build fences to keep people out...and other people build fences to keep people in” (Wilson 61). In a well developed essay, explore the rationales that lead one to build a fence, and explain what the fence offers to the people who reside inside it.
but it must have a perimeter of 1000 m. She wishes to fence of a plot
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