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

Question

asked Oct 6, 2021 211k views

2 Answers

Dan Alvizu · Answer 1 · 2021-10-11T14:29:26+0000

Answer:

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.