Which side lengths form a right triangle? Choose all answers that apply:
А
9, 12, 15
B
2,6,738
3,9, 91

Here is your answer :

For option ( a )

We know that the longest side of any triangle is its hypotenuse.

So, hypotenuse = 15

Other sides = 9, 12

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of Square of other sides

( 15 )^2 = ( 9 )^2 + ( 12 )^2

225 = 81 + 144

225 = 225

Hence,it can be sides of a right angled triangle.

For option ( b ),

We know that the hypotenuse of a right angled triangle is its longest side.

So, Hypotenuse = √38 = 6√2

Other sides = 2 , 6

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of squares of other sides

( 6√2 )^2 = ( 6 )^2 + ( 2 )^2

72 = 36 + 4

72 ≠ 40

So, it can't be sides of a right angled triangle.

For option ( c )

We know the longest side of any right angled triangle is its hypotenuse.

So, Hypotenuse = √91

Other sides = 3 , 9

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of squares of other sides

( √91 )^2 = ( 3 )^2 + ( 9 )^2

91 = 27 +81

91 ≠ 108

So, it can't be sides of a right angled triangle.

The final answer is option ( a ).

Step-by-step explanation: