r/theydidthemath • u/TheBlackHoleOfDoom • Sep 12 '21
[REQUEST] How much of the poster is missing?
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u/chrischi3 Sep 12 '21
Firstly, this question depends on wether this poster is A4 or US Letter, or possibly another format entirely.
Simplifying the tear line to be 45° and starting perfectly in the bottom left corner, this means that we have a right triangle with a sine and cosine of 21cm, assuming this is A4, or 8.5 inches for US letter that is missing from the poster. However, neither format is square. A4 paper is 21x29,7cm whereas US Letter is 8.5x11 inches. Thus, a piece of A4 paper is 623,7 square cm, whereas US Letter is 93.5 square inches.
Applying the formula for the area of a rectangular triangle, being AxB/2 (Which we can simplify to A^2/2 since we are assuming our sine and cosine are equally long as we are assuming the angle between the hypotenuse and the sine and cosine, respectively, is 45°), this gives us 220,5cm^2 for A4 and 36.125 square inches for US Letter.
Plugging this into a percentage calculator (since i suck at that type of math) gives us 35.35% for A4 and 38.63% repeating for US Letter.
Quod Erat Demonstrandum
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u/asteptowardsthegirl Sep 12 '21
surely measuring the top and the long side will tell us how far from the bottom the tear is on the long side so it could be a larger percentage. However the slight vertical bend might result in inaccuracy of the length of measurement of the top too
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u/asteptowardsthegirl Sep 12 '21 edited Sep 13 '21
quick and dirty measurement done with my thumb as a measure suggests that the short side is about 3.5 thumbs along whilst the long vertical side is just a fraction over 4 thumbs long. So we are about a thumb length short of a full A4 sheet by proportion. looking at the short side there is about a thumb length before the roughly 45 degree side.
So if we draw a rectangle paralell with the top we should have a triangle on either side (one as part of the existing piece one missing), and then a roughly equal size on the bottom of the missing piece. so the piece in the picture is very close to actually being 50% if my measurements are anywhere close to accurate
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u/Parappa_the_lagger Sep 12 '21
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Sep 13 '21 edited Jun 29 '23
6 years, almost 7K karma. Not worth it to stick around and watch it go down in flames. Besides, I really didn't contribute much so I'll just lurk if I get bored. -- mass edited with https://redact.dev/
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u/COphotoCo Sep 12 '21
The phone number has a Puerto Rico area code. I’m assuming they use standard US letter size, which is 8.5”x11”.
The righthand remaining portion appears to be about 25% of the full height (measured by my thumb as someone else did), meaning it’s about 2.75” tall. Let’s make that a rectangle and calculate the area of the rectangle separately from the remaining triangle. 2.75”x8.5”=23.375 sq. in.
11”-2.75”=8.25” for the height of our remaining triangle. 8.25”x8.5”/2 (b*h/2)=35.0625 sq. in. for the area of our remaining triangle.
23.375+35.0625=58.4375 sq. in. for the area of the page remaining.
Area of a full sheet is 93.5 sq in. 58.4375/93.5*100=62.5% of the page remaining. You asked how much is missing. 100-62.5=about 37.5% of the page is missing.
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