Thursday, March 09, 2023

I solved this in 30 seconds

Enjoy. You can do the math in your head for this one.





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Posted by Kevin Kim at 3/09/2023 04:05:00 AM

3 comments:

John Mac said...

If there is one thing I am worse at than grammar and punctuation, it is math. My brain just isn't wired that way.

March 9, 2023 at 7:00:00 AM GMT+9
Kevin Kim said...

This PreMath channel on YouTube reminds me of how much I've forgotten. I fail to solve most of the problems on the channel, but every once in a while, an easy one like this pops up, and I can feel temporarily proud.

Sometimes, being "good at math" is simply a matter of common sense, but sometimes, it's more about remembering certain algebraic and geometric properties so you can shortcut your way to a solution.

In the above case, they give the circle's radius as 3√2. Imagine that radius going from one corner of the square to the center, then from the center to the diagonally opposite corner of the square. This gives you double the radius of the circle, i.e., the diameter. It also gives you the length of the square's diagonal: 6√2.

That diagonal divides the square into two right triangles, but not just any right triangles: these are 45-45-90 right triangles. This means that, if the leg length of such a triangle is x, then the diagonal (the hypotenuse) has to be x√2.

Work that logic backward. If the hypotenuse is 6√2 (which we know), then the leg length must be 6. So now, you know the length of the side of the square. To calculate the square's area, just multiply 6 by 6: 36. QED.

March 9, 2023 at 1:17:00 PM GMT+9
John Mac said...

Easy for you to say.

Algebra was torture for me in school, I somehow managed to pass the required course in college, but did not retain anything I'd "learned" after the final exam.

March 10, 2023 at 6:02:00 AM GMT+9

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