Optimizing Measurements

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umard23

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May 25, 2010
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i am not to sure if this is geometry or not so I'm sorry if it's in the wrong topic

i don't get this stuff: perimeter and area Relationships of a rectangle

Heres an example:

A fence is to be built with prefabricated sections that are 2.8m in length. what is the maximum rectangular area that you can enclose with

a) 20 pieces?

b) 40 pieces?

if you can just explain what this stuff is in the first place and what i am suppose to do in general, it doesn't make sense, or even a lesson i would really appriciate it. thanks:)
 
umard23 said:
i am not to sure if this is geometry or not so I'm sorry if it's in the wrong topic

i don't get this stuff: perimeter and area Relationships of a rectangle

Heres an example:

A fence is to be built with prefabricated sections that are 2.8m in length. what is the maximum rectangular area that you can enclose with

a) 20 pieces?

b) 40 pieces?

if you can just explain what this stuff is in the first place and what i am suppose to do in general, it doesn't make sense, or even a lesson i would really appriciate it. thanks:)
Click to expand...

First you need to make some assumption. One assumption is that your fence does not have any "gaps".

Another assumption could be that you'll use only "whole" board - no cutting allowed.

With those in mind let's look at the problem (a)

What length can you cover with 20 boards ? 2.8 * 20 = 56 m

This is your perimeter of the rectangular field to be fenced. ? Why?

Now if that unknown rectangular field had length = L and width = W the perimeter P = 2 * (L + W)

2 * (L + W) = 56

L + W = 28

Since we assumed the boards cannot be cut

L = n * 2.8 (use n boards in the length side)

W = m * 2.8 where 'm' & 'n' are integers.

then

m + n = 10 ? why

Now figure out the possible values of 'm' & 'n' that add up to 10 and then which pair of 'm' and 'n' will give you the largest area.
 
If you can use calculus...

A = lw
(l + w) = 28 after a bit of simplifying

A = l(28 - l) = -l^2 + 28l

dA/dl = -2l + 28 = 0 when l = 14 m.

14 m /2.8 m per section = 5 sections. Therefore, the width must also be 5 sections since the Area is definded as some kind of rectangle.
 
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