(NONE) Given that the sides of the triangle are $50 \text{ cm}, 80 \text{ cm},$ and $100 \text{ cm}.$
To check if it is a right-angled triangle,we apply the converse of the Pythagoras theorem,which states that in a triangle,if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides,then it is a right-angled triangle.
Calculate the squares of the sides:
$50^2 = 2500$
$80^2 = 6400$
$100^2 = 10000$
Now,check the sum of the squares of the two smaller sides:
$50^2 + 80^2 = 2500 + 6400 = 8900$
Comparing this with the square of the longest side:
$8900 \neq 10000$
Since $50^2 + 80^2 \neq 100^2$,the given triangle does not satisfy the Pythagoras theorem.
Therefore,the given triangle is not a right-angled triangle.