Find The Height 'h' In This Shape | Learn Two Easy Methods

[waheisel]

Actually PreMath proves the Cross Ladder Theorem with the first method: If you substitute AE for 5 and BC for 7, instead of getting h=35/12 you will get h=AE*BC/(AE+BC). Then take the reciprocal of both sides and you have 1/h=1/AE+1/BC. I very much enjoy PreMath videos. They are indeed exciting! Thank you sir!

[miltonluoma]

I found a third way to solve the problem. I determined the equations of the lines passing through segments EB and AC and then found the coordinates for point D. Using the form y = mx + b, for EB: y = -5x/B + 5 and for AC: y = 7x/B. We want to find the intersection where y = h. So, solving for the intersection point’s x value in both equations: h = 7x/B so x = hB/7 and h = -5x/B + 5 so x = ((h - 5)B)/(-5). Setting both equations for x equal to each other: hB/7 = ((h - 5)B)/(-5) and simplifying: (-5)hB/7 = (h - 5)B. Divide both sides by B leaves -5h/7 = h - 5 so -5h = 7h - 35 and combining h terms on one side, -5h -7h = -35. -12h = -35 or h = 35/12.

[petersmith]

I used simultaneous equations.
Make "A" the origin, and the length of AB = p. Line AC is expressed as y= 7x/p. Line EB is expressed as y = -5x/p + 5.
The lines interest at a point where x = 5p/12. As y = 7x/p, the coordinates of D are (5p/12, 35/12). So h = 35/12

[MichaelPaoli]

Another way, bit more algebra and less geometry:
place on Cartesian coordiante plane as follows:
A at (0, 0)
B at (AB, 0)
C at (AB, 7)
E at (0, 5)
Determine line formulas for AC and EB, then find y(=h) where they intersect
AC=0+7x/(AB)
y=7x/(AB)
EB=5-5x/(AB)
y=5-5x/(AB)
7x/(AB)=5-5x/(AB)
12x/(AB)=5
x=5AB/12
y=7x/(AB) y=5-5x/(AB)
y=7(5AB/12)/(AB) y=5-5(5AB/12)/(AB)
y=7(5/12) y=5-5(5/12)
y=35/12 y=60/12-25/12
y=35/12 y=35/12 = h = 1+11/12

[michaelmounts]

Love your channel! Every morning, my niece and I watch your channel as she has been out of school due to covid shutdown. Sometimes I learn a lot as well...as in this case. Any books you'd recommend on lesser known geometric theorems as in you second method....thanks in advance.

[theoyanto]

Wow, brilliant... I never knew about the ladder magic, thats very very useful to know thank you so much 👍🏻

[JuliusCesar]

The second method is the same like calculating parallel resistors.

[princejag]

Crossed ladder theorem!!! Fantastic. Could you explain later how the theorem created.

[spafon]

Took me a while but I got it eventually. I like this kind of problem because there is a continuum of solutions in terms of the dimensions of the structure but you can solve for h because it is the same for all solutions. You can arbitrarily stretch the structure horizontally since the only dimensional constraints are on the vertical segments, yet you always get the same h.

[medsalahrhayem]

Excuse me sir, but if we consider the triangle ABC and we apply thales theoreme, we will have :
AF / AB = H / 7, Wich gives H = 3.5 since AC = 1 AB / 2 .
THANK YOU FOR REPLYING !

[Anmol_Sinha]

This can also be done using BPT theorem btw

[sidhusandevamanoharan]

With the information given, i can construct any amount of such figures with one side 5 and other 7. So h will vary depending on the distance between the two sides. Can someone explain the dilemma?

[msafasharhan]

Hallo doctor, we need explanation of the second solution (the theorem of the crossed ladder)

[kaczka]

Similar: draw 3 rays from one point. The angles between rays are 120 grad each. Cut two fragments on the outer rays from the common point of lengths a and b. What is the formula for the length of fragment cut by straight line on the middle ray?

[experimentingalgorithm]

Crossed ladder theorem looks interesting
Please teach us "Reciprocal Pythagoras Theorem"

[math]

a very interesting problem, very well done bro

[Teamstudy]

h = 35/12.VERY very very very very very easy question SOLVED it Long

[mustafizrahman]

I have failed to solve it. But many many thanks for the theorem.

[bullerheden]

Three problems have the same solution:
A) crossed ladders
B) one person can do the job in 5 hours, another in 7 hours. Together it takes ? hours.
C) two resistors 5 and 7 ohms in parallel.
I love PreMath videos.

[enricocarta]

I considered EB and AC two lines and the point A as the origin. I calculated the equations of the two lines and then I calculated where they have the same value