Believe in triangle, not algebra!

0:00 Find the area of the red triangle
2:39 Solutions from my Instagram followers

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#math #algebra #mathbasics

[bprpmathbasics]

More solutions (from my Instagram followers) at 2:39

[labzioui]

6/(b+6)=h/6
h(b+6)=36
Area=h(b+6)/2 =18

[mychaelsmith]

There's nothing special about 6. If the left side of the triangle is a and the bottom right line segment along the bottom edge is b, you can just observe that the "red area" is ab/2.

[zachansen]

Since the answer must be the same no matter how wide the triangle is, pick a convenient width and just say the large triangle's width is 6. Then the small 6-wide right triangle is the big triangle. Then it's just half a 6x6 square.

I'm curious how to do it the opposite way though. What happens as the width of the triangle approaches infinity? The smaller 6-wide right triangle's area goes to zero. But how do you get 18 for the other triangle then? I get the 0*inf indeterminate form and don't know how to proceed.

[mnek]

Love this! Glad you showed geometrically why the area was irrespective of unknown lengths by a skew (the left right triangle being vertically skewed that way).

[anonymouscheesepie]

SIMILAR TRIANGLES:

a/b = c/d

6/(6 + x) = y/6 -> y = 36/(6 + x), where x is the horizontal side of the red triangle to the left, and y is the height of the red triangle on the right

A = .5(6 + x)y
A = .5(6 + x) * 36/(6 + x)

denominator and numerator cancel

A = .5 * 36 = 18

[florianbasier]

You could simply have used Thales and saved your neck some issues. The small triangle (on the right) has sides of 6 and b while the big triangles has sides of (6+h) and 6 so you know 6/(6+h) = b/6 meaning that (6+h)b=36. The area you are looking for is half of base (h+6) times height (b) so A=(6+h)b/2. Now you reinject the results from Thales and A=36/2=18. No need to draw extra lines, no need to break your neck.

[L_Ratio_]

what I did is : let the acute angle at right side be x, in smaller right angled triangle tan(x) = b/6, in the larger right angled triangle tan (x) = 6/(6+h), so b/6 = 6/(6+h). cross multiplying we get b(6+h) = 36 which is base×height of red triangle so area = base×height/2 which is (18).

[jickey]

Just use the side denoted as h, then the required area is 6(6+h)/2 minus 6h/2

The h cancels out to get us 18

[leaDR]

ALTERNATIVE METHOD WITHOUT CONSTRUCTION! :

The bigger triangle will be similar to the smaller triangle thru the AA rule, let the horizontal side we don't know be x and the vertical be y, then, we will get -
6/y = x+6/6

On moving around a bit, we'll get - 36 = xy + 6y

Now if we make it so that 36 is written as 6 x 3 + 6x 3, then

6•3 + 6•3 = xy + 6y

Now we can see that the 6 and six are equal, then it means, we can compare. So, we get that x must be 6 and y must be 3

Now using area of triangle, we get - 1/2 (6+6)x3 = 6x3 = 18 unit^2

[Hzur]

I did it using a computer but I made a system of two equations with x representing the unknown length of the red triangle and y representing the height. One equation was based on the areas, and the other was based on the hypotenuse of the whole triangle. I approximated the answer to be 17, 99997362 or simply 18 if I calculated symbolically instead of numerically.


I just couldn’t figure it out without using this hard algebraic method.

[oldmanwaterfall]

Well since I don't want to brush up on trig, couldn't you use a system of equations, using the base and height of the small triangle within the red triangle and the area of the red triangle?

Edit: just 1 equation needed:
▶️ + 🔺 = Big Triangle
🔺 = Big Triangle - ▶️
🔺 = 0.5*6*(6+x) - 0.5*6*x
🔺 = 0.5*6*6 = 18

Together x and the 6 at the bottom makeup the bottom of the big triangle. Also x makes up the height of the white triangle or ▶️

[AverageCommentor]

If we set the unknown part of the base equal to x, the area of the whole thing is 18+3x. We can work out that the area of the white portion is just 3x by the fact the perpendicular height must be equal to x. So the area of the red is 18+3x-3x = 18 (units squared).

[jubinsoni]

I don't remember exactly but a similar question was there in my 8th class NCERT maths book

Thanks for sharing

[PowerShellWizard]

Usually bprp videos are crystal clear, but not this one. I am still struggling to wrap my mind around how the slanted triangle has an area of the shaded triangle. I am an Electrical engineer and I spent some time trying to figure this out but still can't. @bprp math basics, perhaps you can explain this a bit better? Thanks!

[rebokfleetfoot]

geometry is so cool, i could do it all day

[sleepy.]

I looked at it from the similar triangles perspective but bprp's way is cooler!

[Elaalan_lol]

Pls explain this question!!! :

' The centrifugal force is
a) a real force.
b) opposite force of centripetal force.
c) a virtual force.
'

AI says it's option c and my teacher says it's option b.

[JeffreyJohnson-vv]

Miller Sarah Hernandez Charles Garcia Ruth

[hikari]

I always thought the height jad to be perpendicular to the base!
I'm lost la