Question

Which side lengths form a right triangle?
Choose all answers that apply:

A.9, 12, 15

B. 2, 6, sqrt(38)

C. 3, 9,sqrt{91}

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Answer 1

Hey Mate !!

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.


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The final answer is option ( a ).


Hope it helps !!

Answer 2

Answer:

options is a ,