Geometry Using Properties of Similar Triangles (Ratios & Algebra) Missing Area #shorts #math #maths

[cannypride]

Me: Too easy, I solved it in 1 second

Also me: Just multiply every number you can see

[daextraxtor]

》A = xy = Area of large triangle - Area of small triangles = (x+3)(y+4)/2 - 4x/2 - 3y/2
》xy = (xy + 4x + 3y + 12 - 4x - 3y)/2
》xy = xy/2 + 6
》xy/2 = 6
》A= xy = 12

[paulhill]

I'm 70, and I enjoy these immensely. Keeps me sharp. I get about 2 out of 3 correct.

[wordysafe]

You can also multiply the equation diagonally and get the answer
4/x = y/3 => x • y = 4 • 3

[xdifficultviper]

Bruh one of the answers is just “no thanks”💀💀 that’s awesome

[seeven]

It's much easier to cross multiply. (A/B = C/D, A*C = B*D. Given 4/x = y/3, 4*3 = x*y, so the area must be equal to 12

[RizwanKhan-ibxh]

Or use,
Area of triangle = (x+3)*(y+4)/2

Thus, Area of Rectangle = (x+3)*(y+4)/2 - (3y) /2 - (4x) /2

Therefore,
xy = (xy + 3y + 4x + 12 - 3y - 4x) /2

Thus, xy = ( xy + 12 )/2

Hence, 2xy = xy + 12

Finally xy = 12 .

[TVkachu]

This was a genuinely interesting question

[anttivalimaki]

X1=kx2. X1^2=k^2x2^2 When needed area proportion can be expressed length proportion squared when geometrically so called zoomed situations. Can be seen of k squared, must relate to area proportion.

[CrimsonFlameRTR]

“So let’s see if they’re similar. Two triangles are similar if they have all of the same angles. So have a right triangle here. We have some angle here, and we have another angle here that’s going to be the same.”

LOL. Nice proof.

[theanalyzer]

You can also make the triangles squares
It becomes 4*4 and 3*3. You will realise that the missing portions of the square is equal to the rectangle. And that the missing portion is equal to 4*3

[gettingbetterlife]

Tbh I think you made this WAY more complicated than it needed to be XD

[alfedrale]

I found a way to complicate it more by comparing it to a third triangle which is the 60 30 90 one. I just squared the adjacent and opposite to get the hight of the small one. Then I just multiplied 3*4 (cuz4×1=4) and that's it.

[kentagent]

a/b = c/d <=> ad = bc. Not sure what the point of the extra steps were when you could've gone directly from 4/x = y/3 <=> xy = 4*3

[jeal]

This one's actually hard for me yet fascinating to see the solution

[evanjones]

Take expression of total length of large triangle and subtract it from expression of length of rectangle. Plug them into area of a rectangle… A = xy

(4+y)-y * (3+x)-x = 12

[neerajaneja]

Also 6, 8, 10 are Pythagorean triplets
So, x+4=8, y+3=6 so xy=12

[Torcuga]

If we divide the quadratic formula by pi to the eighth power, subtracted the cubed root of the constant of proportionality, then we can see that the answer is E.

[thomasjensen]

My brain just melted like mercury flowing out of a thermometer.

[shashiprabha]

Nice method, i am happy to see the real maths methods not a gimmick or a trick.