Question

show that a^2+b^2,a^2-b^2 and 2ab is the sides of right angle triangle

Answer 1

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Answer 2

Answer:

Let the sides be AB = a ^2 + b ^2, BC = a ^2 - b ^2, CA = 2ab

BC ^2 + CA ^2 = ( a ^2 - b ^2 ) ^2 + ( 2ab ) ^2

BC ^2 + CA ^2 = a ^4 - 2 a ^2 b ^2 + b ^4 + 4 a^2 b ^2

BC ^2 + CA ^2 = a ^4 + 2 a ^2 b ^2 + b ^4

BC ^2 + CA ^2 = ( a ^2 + b ^2 ) ^2

BC ^2 + CA ^2 = AB ^2

Hence, the sum of the squares of the lengths of two sides is equal to the square of the length of the third side.

This is possible only in a right angled triangle.

Hence ∆ ABC is right angled.