Calculate the Length of the Side of the Square ABCD | Step-by-Step Explanation

[sangam]

Waww .... Amazing video ... U have just a Einstein Brain sir ... ❤

[johnbrennan]

So thankful to this wonderful man for keeping our minds concentrated on so many math problems.

[philipkudrna]

Did it in my head in 30 sec. Once you comprehend that you need to „straighten“ the middle side into one large right triangle, the rest is a piece of cake as 50 is clearly the sum of 25+25, which means the side is 5. But as always: a good and very clear explanation!

[math]

Got it. I extended BE. This is a great brain teaser for students involving multiple operations. Excellent presentation.

[erichanastacio]

Once you've made the Line BP at time 1:50 being "the hypotenuse" of the small and big right triangles, the answer dawned up to me within the next 40 seconds.
Thank you.

[benv]

The zig-zag is symetrical. If you were to flip the zig-zag so that the piece that is 1 extends to the corner "C", it's length would be 4 as well. You have a 3, 4, 5 triangle.
QED (Quite easily done) :)

[crustyoldfart]

There is a simple construction which makes for a familiar shape : Construct a central unit square abcd ; starting with b ; b lies on the extended line segment through B and Bb = 4. Similarly a lies on extended line segment Aba and Aa = 4, Similarly construct points c and d such that Cc=4 and Dd = 4,
The result is ab=1, bc=1 cd=1 da=1. It will be noted that 4 right triangles have been constructed - namely AbB, DaA, CdB, and BbA. Each of these is a 3, 4, 5 triangle and AB=BC=CD=DA=5.

[canadiannuclearman]

I did this in my head. I was a draftsman for 30 years.

[זאבגלברד]

Thank you. Good idea. Please let me suggest two more ways. One is that DB creates two right-angle similar triangles. Second is to put it in a coordinate system: D(0, , 0) then a point at (4, 0) then a point at (4, -1) then B(7, -1) and use diatance formula.

[devondevon]

I got '5' differently by constructing two RIGHT triangles using 8:01
'4' AND '0.5 ' and '3' AND '0.5' as 0.5 one-half of 1 and since the diagonal of the square passes through 0.5. I then find the hypotenuse of these two triangles.
So for the top triangle, it is the square root of 4^2 + 0.5^2 or sqrt (16.25)=4.0311
and for the bottom triangle, it is the square root of 3^2 + 0.5^2 or sqrt (9.25)=3.0413
Then add (4.0311 + 3.0413) to get 7.0725 .
Then a^2 + a^2 = (7.0725)^2
2a^2= 50
a^2=25
a=5 answer.

[TazPessle]

Rearrange the lines to have a 1 by 7 rectangle having a shared diagonal with the square: √50. 5 pops out pretty quick from there.

[musharrafali]

Amazing and useful video for learners.

[vincie]

This is easy, when I see a 3 and 4, i know 5 must be coming next

[blumobean]

I love Pythagoras. Worked another one.

[hectorheslop]

What is the formula for the diagonal of square ABCD, of known side measurement .

[gillardinpascal]

Draw the square EFGH (EF=FG=GH=HE=1) in the middle.
Four identical triangles : FDC, ECB, HBA, GAD
FDC : FD=4 ; FC=3
Pythagore => DC² = 4² + 3² => DC² = 25 => DC = 5

[lcr]

DE and BF are hypotenuses - Pythagoreern theorem must be applied. Then please apply Ptolemy's theorem to find DB in diamond DEBF. Then all is very easy, as you did. No additional construction must be applied :). All the best!

[mcwulf]

The diagonal is the diagonal of a 7*1 rectangle. Did this in my head in seconds.

[venkatk]

So simple! Only after seeing the solution..

[terryjohinke]

Now that's "thinking outside the square"!