A beautiful use of Pythagorean triplet

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Hello math bugs(šŸž) and hivers(šŸ)
I hope you are strong amd stout and doing great in life

Well come to another intersting gemetric problem and its solution. āˆ†ABC is a random triangle. AD is perpendicular to BC and E is a random point on AD. If *AB =10 cm , AC= 17 cm and CE =16 cm, What is BE? Check the figure down below:

This is a true use of pythagorean triplet .Today we need no other concept except it. If we use pythagorean trip on triangles on the problem figure, a sweet relation must come out and whcih is given by ABĀ²+ CEĀ² = ACĀ² + BEĀ². I'll proof it, once we get to the answer.

Check the following window for value of be BE

Let's prove it

We gonna use pythagorean triplet in āˆ†ABD and in āˆ†CDE.

From āˆ†ABD
We have ABĀ² = ADĀ² + BDĀ²...equation (1)

From āˆ†CDE
We have CEĀ² = CDĀ² + EDĀ²...equation (2)

Now, after adding equations (1) and (2)
We have ABĀ²+ CEĀ² = ADĀ² + CDĀ² + BDĀ² + EDĀ²...eqn (3)

Again, using pythagorean teiplet on āˆ†ADC and āˆ†BDE,
We can say

ADĀ² + CDĀ² = ACĀ² and BDĀ² + EDĀ² = BEĀ²

Now, if we replace ADĀ² + CDĀ² and BDĀ² + EDĀ² in equation (3) by ACĀ² and BEĀ² respectively, we can have

ABĀ² + CEĀ² = ACĀ² + BEĀ² (proved)

Check the following figure also if you missing out something

For replacing check this one

All the figure are used here made by me using android application. There may be some construction misatke(s) or they may not be proper drawing. It takes time to make those figure. If you find any dispute, please ingnore it and cosider the data only.

I hope you find this post interesting and understandable.

Thank you so much for visiting

Have a nice day

All is well

Regards: @meta007

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11 comments
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@meta007...


Hello there! It was good to chat with you today at The Terminal. I do hope you feel better now, after our explanation of the voting situation! Sometimes... people will be people! All we can do, is keep being ourselves. Anyway... as I mentioned; it's not that I don't appreciate mathematics. I know it is in everything we do... I just lose patience when we go past 1 + 1 = 2 lol. I remember the days of going to college online for my B.S. in IT. At one time, we were studying the concept of Relational Algebra, and the statement, "Relational Algebra, is the backbone of Microsoft SQL Database querying". This, of course, left me with that "deer in a headlight" expression... but I tried my best, to understand what was being taught. Now then... I did look this mathematical equation up and found the following information "Identify Common Pythagorean Triples" for Dummies lol. From this link, I found the following statement:


"A Pythagorean triple is a list of three numbers that works in the Pythagorean theorem ā€” the square of the largest number is equal to the sum of the squares of the two smaller numbers. The multiple of any Pythagorean triple (multiply each of the numbers in the triple by the same number) is also a Pythagorean triple. They seem to reinvent themselves."

Source


Okay... but can we get another example? I went to YouTube and found this video with the awesome Ken Au... check this one out:



Another example of the Pythagorean Thereom, to help others understand. Regardless... this has certainly got my brain thinking! Hopefully, others will gain a better understanding of this concept... appreciate your continued energy to help everyone on the blockchain understand math. Hope you had a wonderful weekend, my friend!

!LUV

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Thanks for taking time to write wonderful comment. Really, this triplet has a lot of uses.

I must check the video you shared. I had a post about it in details long ago. The link is here

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!WINE

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Thanks for the drink. Though I don't drink regularly šŸ˜­

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I've never been too good at maths, let alone trigonometry, but I really enjoyed seeing this kind of post in this niche, and how you've demonstrated the beauty of the argument you make in your post. Really fascinating.

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I am glad that you liked it. Thanks for your sweet words man. Have a good day.

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