Math CentralQuandaries & Queries


Question from Jas, a student:

Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:

****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??

I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didn't get the same answer!

Hi Jas,

Suppose you have a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$. Write down Pythagoras' Theorem for this triangle.

Draw a semicircle on each of the sides of the triangle. What are the radii of the semicircles? What are the areas of the semicircles on the two legs? What is the sum of these areas. Simplify using the Pythagorean relationship you found above. What did you get?

Write back if you need more help.


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