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For a maths project, we are designing a house. One of the elements of this is the fencing, and we need to calculate the cost of fencing per linear meter. The information that I have is that a $137$mm $\times$ $23$mm plank of wood that is $5.4$ metres in length is $ \$72.63$ per square meter. How do I figure out the price of the plank of wood per linear meter?

Rick
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Maths
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  • Which way are you measuring the area of a plank? $5.4 \times 0.137$ square metres or something else? What counts for length - the fence or the plank? And if it is the fence then how high will the fence be? – Henry Jun 11 '20 at 09:25
  • The fence would have a constant height? Then the length would be the area divided by the height – Dhanvi Sreenivasan Jun 11 '20 at 09:28
  • @Henry, the plank has a width of 0.137 meters, a length of 5.4 meters and a depth of 0.023 meters. This means that the area of the plank is 5.4 x 0.137. The height of the fence will be 5.4 meters and the dimensions of the plank are all that is needed to be known because once I know the price of a linear meter of wood (so not necessarily the actual plank), I can apply that to the dimensions of the fence to find the price of the fence. I hope that this is helpful! :) – Maths Jun 11 '20 at 09:31

1 Answers1

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We need to first figure out which of the three dimensions is the one that we wish to know the price per linear meter of. Since the fence will be $5.4~\text{m}$ tall (constant), that dimension is not what we're interested in. Rather, the real question is: how wide (long) will the fence be? Can we make it go around the house? Those are the practical questions that we have in mind.

The dimension that contributes to the length of the total fence is the quantity $137~\text{mm}$. That's because the planks are usually set up so that $\text{height}>\text{width}>\text{depth}$.

Furthermore, I believe that the price of a single plank is based on the largest cross-sectional area of a single plank, that is $0.137~\text{m}\times 5.4~\text{m}$. A single plank will cost $$ (72.63~\frac{\text{\$}}{\text{m}^2}) \cdot (0.137~\text{m}\times 5.4~\text{m}) \approx \$ 53.73 $$

Sounds quite expensive. Anyway, now the price of the fence, per meter, is $$ \frac{ (72.63~\frac{\text{\$}}{\text{m}^2}) \cdot (0.137~\text{m}\times 5.4~\text{m}) }{ 0.137~\text{m} }\approx \$392.20 $$

Logically, this makes sense because we know that the fence will be 5.4 meters tall, and we know the price per square meter. So it should just be multiplied by the height in meters.

Matti P.
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