SOLUTION: how do I understand Pythagoras theorem

Question 1132769: how do I understand Pythagoras theorem
Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
construct squares with sides equal to each side of the right triangle
:
you then have three squares
:
how do you find the area of a square?
:
the sum of the areas of the smaller squares is equal to the area of the square whose side is the hypotenuse of the right triangle
:

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The Pythagorean Theorem
If and are the lengths of the legs of a right triangle and is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This theorem holds true for this right triangle—the sum of the squares of the lengths of both legs is the same as the square of the length of the hypotenuse. And, in fact, it holds true for all right triangles.

This relationship is represented by the formula:

The Pythagorean Theorem can also be represented in terms of area. In any right triangle, the area of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs. You can see this illustrated below in the same 3-4-5 right triangle.

Note that the Pythagorean Theorem works with .

You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle’s other two sides, called the legs. Put another way, if you know the lengths of and, you can find .

In the triangle above, you are given measures for legs and: and , respectively. You can use the Pythagorean Theorem to find a value for the length of , the hypotenuse.

Using the formula, you find that the length of , the hypotenuse, is .

another example:
A soccer field is a meters wide and meters long. The coach asks players to run from one corner to the corner across the field. How far do the players run?

diagonal divides rectangle into two right angles and for each of them diagonal represents a hypotenuse, and legs are and of a soccer field
so,

answer: the players will run

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