Answer:
The correct answer is A. [tex]4^{2} +12^{2} \neq 13^{2}[/tex]
Step-by-step explanation:
A right angled triangle is the type of triangle in which one of the three angles is [tex]90^\circ[/tex].
For a triangle to be right angled triangle, following equation must hold:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}[/tex]
Where Hypotenuse is the largest side of triangle and is opposite to the angle with value [tex]90^\circ[/tex].
Base and Height are the two other sides making an angle of [tex]90^\circ[/tex] with each other.
In the given question figure, largest side, XY = 13 units
Other two sides are:
YZ = 4 units
XZ = 12 units
For this [tex]\triangle XYZ[/tex] to be right angled, the following must be true:
[tex]XY^{2} = XZ^{2} + YZ^{2}[/tex]
[tex]XY^{2} = 13^{2} = 169[/tex]
[tex]XZ^{2} + YZ^{2} = 12^{2} + 4^{2}\\\Rightarrow 144 + 16\\\Rightarrow 160[/tex]
[tex]160 \neq 169[/tex]
Hence, the given triangle is not a right angled triangle because of following:
[tex]4^{2} +12^{2} \neq 13^{2}[/tex]
Hence, option A. is correct answer.
