Question

I need the derivation of pythagoras theorem . Kindly don't send the answer h^2 = b^2 + p^2 . Show me how to derive this formula . Experts do give me my answer .; I need the derivation of pythagoras theorem . Kindly don't send the answer h^2 = b^2 + p^2 . Show me how to derive this formula . Experts do give me my answer .

Answer 1

What is the Pythagorean Theorem?
You can learn all about the Pythagorean Theorem, but here is a quick summary:

triangle abc
The Pythagorean Theorem says that, in a right triangle, the square of a (a2) plus the square of b (b2) is equal to the square of c (c2):

a2 + b2 = c2

Proof of the Pythagorean Theorem using Algebra
We can show that a2 + b2 = c2 using Algebra

Take a look at this diagram ... it has that "abc" triangle in it (four of them actually):

Squares and Triangles
Area of Whole Square
It is a big square, with each side having a length of a+b, so the total area is:

A = (a+b)(a+b)

Area of The Pieces
Now let's add up the areas of all the smaller pieces:

First, the smaller (tilted) square has an area of: c2

Each of the four triangles has an area of: ab2
So all four of them together is: 4ab2 = 2ab

Adding up the tilted square and the 4 triangles gives: A = c2 + 2ab
Both Areas Must Be Equal
The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:

(a+b)(a+b) = c2 + 2ab

NOW, let us rearrange this to see if we can get the pythagoras theorem:

Start with: (a+b)(a+b) = c2 + 2ab
Expand (a+b)(a+b): a2 + 2ab + b2 = c2 + 2ab
Subtract "2ab" from both sides: a2 + b2 = c2

DONE!

Now we can see why the Pythagorean Theorem works ... and it is actually a proof of the Pythagorean Theorem.

This proof came from China over 2000 years ago!

There are many more proofs of the Pythagorean theorem, but this one works nicely.