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The Mathematics of Scale

April30

model2Hey – do you enjoy making model cars, boats, planes, dolls houses, or even F1 racing cars? Modelling is great fun and most model kits come with a scale on the front of the box, such as 1:50 or 1:100. I recently saw a modelling kit of the Starship Enterprise, which had a scale or a whopping 1:1000! Scale is expressed as a ratio, such as another model kit of a racing car, which checked out with a ratio (aka scale) of 1:24. 1:24? How did the manufacturers work that out? Why not a ratio of 1:25? H3 can only guess that, after all the machining of the model parts was done, that it was more accurately a scale of 1:24 and not 1:25? Who knows?

Anyway, this idea of scale is an essential part of learning Mathematics in Junior High, and is widely used in many occupations. Architects do their plans to scale and so do map makers. You see scale models of new buildings and engineers and builders have to read scale drawings all the time. So, it is a great skill for mathematicians like you to also have.

modelbox1

Did you know that a young guy called Luca Iaconi-Stewart recently made a scale model of a Boeing 777 entirely out of manila folders? He used a scale of 1:60 which makes his nearly six-year project around 4 feet long. So, the real Boeing 777 would be 60x4ft = 240ft or approx. 73m long. Now that takes a bit of storage space! Check out some more Iaconi’s amazing work here.
model777a(Images used with permission)
777b

 

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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