Question

If a triangle has side lengths \[6,8,10\]is it a right angle ?

Answer 1

Hint: A right Angled triangle is a type of triangle whose one of the three interior angles is .The sides that include the right angle are perpendicular and base .The third side is called the Hypotenuse .Hypotenuse is longest of all its three sides .
Pythagoras theorem states that the square of hypotenuse is the sum of the square of the perpendicular and the square of the base of a right angled triangle.

Complete step-by-step answer:
Here the given sides are \[6,8,10\]
As we know hypotenuse is the longest of all its three sides,
 Therefore, we can let hypotenuse\[ = 10\],
And let perpendicular be \[6\]and base be \[8\]
So now according to Pythagoras theorem, we know
\[{\left( {Hypotenuse} \right)^2} = {\left( {Perpendicular} \right)^2} + {\left( {Base} \right)^2}\]
So applying this theorem with the given values to check whether it is a right angled triangle
L.H.S\[ = \] \[{\left( {10} \right)^2}\]
0r L.H.S \[ = \]\[100\]
Now R.H.S\[ = \]\[{\left( 6 \right)^2} + {\left( 8 \right)^2}\]
Or R.H.S\[ = \] \[36 + 64\]
Or R.H.S\[ = \] \[100\]
As L.H.S\[ = \]R.H.S
Therefore we can say that it is a right angled triangle.

Note: The longest side should be taken as a hypotenuse. And while doing Pythagoras theorem we should be careful in calculating the square of hypotenuse, perpendicular and base .A scalene triangle and an isosceles triangle can be a right angled triangle. If the question is reversed that we are given two sides of a right angled triangle and we have to find the third side, we can use the pythagoras theorem provided that the position of the right angle is known to us.