The Pythagorean to organize was named after well known Greek mathematician Pythagoras. 

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

The 2nd figure listed below helps united state to see why the formula works.

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

Notice the the red square has actually 2 triangle in it and the blue square has additionally 2 triangles in it.

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

You are watching: A square plus b square equals c square


Therefore, area that red square  + area of blue square = area of black square

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

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

Let c = the length of a side of the black color square

Therefore, a2 + b2 = c2


Generally speaking, in any right triangle, allow c it is in the size of the longest next (called hypotenuse) and also let a and also b it is in the length of the other two sides (called legs).

The theorem says that the length of the hypotenuse squared is equal to the size of side a squared add to the length of side b squared.Written together an equation, c2 = a2 + b2Thus, offered two sides, the 3rd side can be uncovered using the formula.We will highlight with examples, but before proceeding, you must know exactly how to discover the square source of a number and also how to fix equations making use of subtractionExercise #1
Let a = 3 and also b = 4. Find c, or the longest sidec2 = a2 + b2c2 = 32 + 42c2= 9 + 16c2 = 25c = √25The sign (√) method square rootc = 5 practice #2 Let c = 10 and a = 8. Uncover b, or the various other leg.c2 = a2 + b2102 = 82 + b2100 = 64 + b2100 - 64 = 64 - 64 + b2 (minus 64 native both sides to isolate b2 )36 = 0 + b236 = b2b = √36 = 6 practice #3 let c = 13 and also b = 5. Discover ac2 = a 2+ b2132 = a2 + 52169 = a2 + 25169 - 25 = a2 + 25-25144 = a2 + 0144 = a2a = √144 = 12

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