Question

Which of the following statement justifies why the triangle shown below is not a right triangle?

Answer 1

its A

Step-by-step explanation:just took test and got 100%

Answer 2

The correct answer is A.
`4^(2) +12^(2) \\eq 13^(2)`

Explanation:

A right angled triangle is the type of triangle in which one of the three angles is
`90^\circ`.

For a triangle to be right angled triangle, following equation must hold:

`\text{Hypotenuse}^(2) = \text{Base}^(2) + \text{Height}^(2)`

Where Hypotenuse is the largest side of triangle and is opposite to the angle with value
`90^\circ`.

Base and Height are the two other sides making an angle of
`90^\circ` 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
`\triangle XYZ` to be right angled, the following must be true:

`XY^(2) = XZ^(2) + YZ^(2)`

`XY^(2) = 13^(2) = 169`

`XZ^(2) + YZ^(2) = 12^(2) + 4^(2)\\\Rightarrow 144 + 16\\\Rightarrow 160`

`160 \\eq 169`

Hence, the given triangle is not a right angled triangle because of following:

`4^(2) +12^(2) \\eq 13^(2)`

Hence, option A. is correct answer.