Question

Question 4 (i)
Given three side of a triangle can be the sides of a right angled triangle or not?
2.5 cm, 6.5 cm, 6cm
In case of right angled triangle, identify the right angle.

Answer 1

Let us consider, the larger side be the hypotenuse and also using Pythagoras theorem,
$(Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$
2.5 cm, 6.5 cm, 6cm

$In\Delta ABC,(AC{)}^2=(AB{)}^2+(BC{)}^2$
$L.H.S.=(6.5{)}^2=42.25cm$
$R.H.S.=(6{)}^2+(2.5{)}^2=36+6.25=42.25cm$
Since, L.H.S. = R.H.S.
Therefore, the given sides are of the right angled triangle.
Right angle lies on the opposite to the greater side 6.5 cm, i.e., at B.