missing numbers in word problem???

[kkhewett]

1. John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing?
I am lost as to how to go about answering this problem.
I realize that I could take 2*L + 2*W = 150 meters but how do I know how to divide up the L and W if I have no numbers to use??
Or could the problem be asking me to convert meters to feet to get a lower number? I am very confused and lost on htis one. Some helpful hints would be nice.
KK

 

[Mrspi]

1. John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing?
I am lost as to how to go about answering this problem.
I realize that I could take 2*L + 2*W = 150 meters but how do I know how to divide up the L and W if I have no numbers to use??
Or could the problem be asking me to convert meters to feet to get a lower number? I am very confused and lost on htis one. Some helpful hints would be nice.
KK

The AREA of the field is to be 150 square meters. For a rectangle,

area = length * width

If we let L = length, and W = width, then we have
A = L*W
and if the area is 150 square meters,

150 = L * W

And you're right, the formula for the perimeter is

P = 2L + 2W

From the fact that

150 = L * W, you can solve for either L or W in terms of the other variable. If I choose to solve for L in terms of W, I can divide both sides of that equation by W:

150 / W = L

Now, substitute (150 / W) for L in the perimeter formula:

P = 2(150 / W) + 2W

You want whole number values for L and W which satisfy
150 = L*W
and
P = 2(150/W) + 2W
which give you the smallest value for P.

Now...I don't know what you've been studying in class, or what level of math you're comfortable with, so I'm not going any further.

Hopefully, this will give you something to start with.

 

[kkhewett]

Thanks a million that does help a ;ot. The class is math for educators and it is a lot of logic, patters etc. Not very fun so far... but I am trying. This is the only problem that has thrown me for a ringer and I think it is in the wording.
Thanks again
KK

 

[wjm11]

1. John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing?
I am lost as to how to go about answering this problem.
I realize that I could take 2*L + 2*W = 150 meters but how do I know how to divide up the L and W if I have no numbers to use??

First, “2*L + 2*W = 150 meters” shows you are confusing area and perimeter. Your equation is saying that the perimeter is 150 m, but the problem does not say that. It says the area is 150 m^2.

Let’s list the problem information and requirements:

A = (L)(W) = 150 m^2

L and W must both be natural numbers.

2L + 2W must be a minimum.

One method to solve this is to build a table of all the possible L and W pairs whose product is 150, then compute 2L + 2W for each pair to find the smallest. I’ll get you started:

(L)(W) = 150
150(1) = 150
75(2) = 150

Can you continue?