The Pythagorean theorem was called after renowned Greek mathematician Pythagoras.

It is vital formula that claims the following: a2 + b2 = c2

The 2nd figure below helps us to see why the formula works.

Did you make the following crucial observation? The figure listed below may help!

Notice that the red square has 2 triangle in it and also the blue square has likewise 2 triangles in it.

The black square has actually 4 that the exact same triangle in it.

You are watching: A squared times b squared equals c squared Therefore, area of red square  + area that blue square = area of black color square

Let a = the length of a side of the red square

Let b = the length of a side of the blue square

Let c = the size of a next of the black square

Therefore, a2 + b2 = c2 Generally speaking, in any right triangle, let c it is in the length of the longest next (called hypotenuse) and let a and also b be the length of the various other two political parties (called legs). The theorem states that the size of the hypotenuse squared is same to the size of side a squared to add the length of side b squared.Written together an equation, c2 = a2 + b2Thus, provided two sides, the third side have the right to be discovered using the formula.We will highlight with examples, but prior to proceeding, you should know how to discover the square root of a number and also how to deal with equations utilizing subtractionExercise #1
Let a = 3 and b = 4. Find c, or the longest sidec2 = a2 + b2c2 = 32 + 42c2= 9 + 16c2 = 25c = √25The authorize (√) means square rootc = 5 exercise #2 Let c = 10 and a = 8. Find b, or the other leg.c2 = a2 + b2102 = 82 + b2100 = 64 + b2100 - 64 = 64 - 64 + b2 (minus 64 indigenous both political parties to isolate b2 )36 = 0 + b236 = b2b = √36 = 6 exercise #3 let c = 13 and b = 5. Find ac2 = a 2+ b2132 = a2 + 52169 = a2 + 25169 - 25 = a2 + 25-25144 = a2 + 0144 = a2a = √144 = 12

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