Art of Problem Solving: Isosceles and Equilateral Triangles

Art of Problem Solving's Richard Rusczyk explores isosceles and equilateral triangles.
Love math? Learn more: bit.ly/ArtofProblemSolving

[@emmagracecooks6827]

this was an extraordinary video!! it was very interesting and educating! you are an awesome teacher!

[@michaelclark3722]

Great video! I'm prepping for the GRE, and this was very helpful

[@juliebsdca]

This video is part of the AoPS Prealgebra series, which was written for kids, particularly to challenge and inspire them beyond the traditional, boring Prealgebra curriculum. I teach kids as young as 5th grade who find his videos motivating and inspiring, challenging them to explore math in ways they never did before. I often learn something new from how he presents things, but I always know the videos were not recorded for adults, so his style obviously reflects that.

[@rhyswilliams7376]

You can simply just go 15^2 - 9^2 = 144 (because you are finding the smaller side), then square root 144 to equal 12. Just making it simple.

[@andrewelliott860]

144(12x12) +441(21x21) = 585 (find this times this equals 585), Ans; 24.182 pixels

[@nitamilin9249]

Thank you so much.

[@mindyourown1898]

this was helpful!!! 2021!

[@danielfalsafizadeh338]

Thank You

[@andrewelliott860]

5x5 spreadsheet compared to a 21x12 spreadsheet, its amazing

[@obelia13sawkins71]

thanks!

[@SumanGhosh-ef3ug]

Thanks sir

[@lakmingunawardena3508]

when a perpendicular drawn from the vertex to the base, the base bisects !!!!!!!! you are good but you are making it more complex

[@Z3nHolEminD]

'' Are you still watching Math videos on youtube from 2015? '' ... me- No from 2012

[@SumanGhosh-ef3ug]

Good sir

[@edwardtambajabba8036]

Can you teach me more

[@newtonle9322]

h=(s/2)*sqrt(3)

[@andrewelliott860]

PixelMAthswilldoit inches and centimeter conversions are already done for u

[@andrewelliott860]

row 21 pixels; column 12 pixels; wot is the angle that dissects the unequal square object I gave you, a = 24 b = 24 c=24 pixels half = 12 pixels, 12 pixels equals one-eighth of an inch, 96 the equals inch, 1 inch = 2.54mm excel spreadsheet x"y theory/tool for education. need one, look wot a teacher can do, count in pixels, teach in pixels, insight. oh terminology dissects = half, quarter etc

[@diveshbhatia8652]

how that 12.9 came?

[@Danielmieczyslaw]

you confusing with square root .why you don't use numbers instead of square root

[@Jay-629]

Because the square roots don’t come out to numbers. He’s not going to write out the entire irrational number-that’s impossible- so he writes square root [number].

[@sisterjimin-ahshalallifegu8211]

I’m lost

[@Stephen-lt1tp]

Lost me at square root of 108..it's not even

[@ewinter9021]

its not sqrt of 108 though. That 108 is the area. He did ((12 * 18) / 2) = 108 Steps to take: s1: divide triangle in half, then do pythagorean theorem on 1 half s2: do 15 sq = 9 sq + h sq s3: get 225 = 81 + h sq s4: get variable h alone, so do 225 - 81 and that leaves: 144 = h sq s5: take the sqrt of 144 and h sq s6: that will leave you with: 12 = h now you have all sides. He then checked his result by doing: s1: (12 * 18 ) / 2 which gives 108, this is the area (half base * height) Hope this break down helps you. Note: sqrt = square root, sq = squared,

[@nomcebozulu2583]

sekuyasa-ke manje

[@RudeDudeMikeTMTheRudeDudes]

Nope