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asked Dec 8, 2015 in CALCULUS by anonymous

1 Answer

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The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse.

Draw a square and inscribe a small tilted square inside it.

image

Observe the figure:

Whole figure is divided into four triangles and a square.

Side of the outer square is image.

Find the area of the big square.

Area of the square is image.

image.

Find the area of the pieces.

Find the area of the tilted square.

Side of the tilted square is image.

Area of the tilted square is image.

Find the area of the four triangles.

Area of the each triangle is image.

Area of the four triangles is image.

Sum of the areas of tilted square and four triangles is image.

Area of the larger square is equal to Sum of the areas of tilted square and four triangles.

Therefore, image

image

image.

Thus , the theorem is proved.

answered Dec 9, 2015 by cameron Mentor

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