Question

complete work to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle

Answer 1

we can prove this by converse of Pythagoras theorem

as ""if the square of one side of a triangle is equal to the sum of square of the other two sides then only it's a right angle triangle and the angle opposite to the longest side is 90°.""

so if we take square of any of the numbers one by one,

${15}^{2} = \: {9}^{2} + {12}^{2} \\ 225 = 81 + 144 \\ 225 = 255$

hence LHS= RHS

so , there can be a right angle triangle from this side with 15 unit side as hypotenuse.