Figure 1.34: Develop a new verification of the Pythagorean theorem using the dia

Question

Figure 1.34:
Develop a new verification of the Pythagorean theorem using the diagram in Figure 1.34. Observe that the figure contains four right triangles and a square, but the configuration is different from that in Figure 1.3 Now we have a large square in a tilted position inside the main square. Usingthe labels provided in the figure, observe that the area of each right triangle is ab/2. And the area of the inside square is e. Finally, the area of the large, outside square is (a b)2. Put all this information together to derive Pythagoras's formula.

Explanation / Answer

From given figure,

Area of larger square = (side)2 = (a+b)2 = a2 +2ab +b2  --> 1)

Area of one traingle = Base*height/2 = ab/2

Total number of traingles = 4

Thus total area of 4 traingles = 4*ab/2 = 2ab --> 2)

Area of inner square = side2 = c2 -->3

Area of outer square = Area of 4 traingles + Area of inner square (As seen in the figure)

Putting 1), 2) and 3) we get

a2 +2ab +b2 = 2ab + c2

Thus,

a2 + b2 = c2 which is Pythagoras theorem

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