Question

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.
[2 marks]

Answer 1

Let us consider, the larger side be the hypotenuse.
Using Pythagoras theorem,
$(Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$
[0.5 marks]

2.5 cm, 6.5 cm, 6cm

$In\Delta ABC,(AC{)}^2=(AB{)}^2+(BC{)}^2$
$L.H.S.=(6.5{)}^2=42.25cm$
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$R.H.S.=(6{)}^2+(2.5{)}^2=36+6.25=42.25cm$
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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.
[0.5 marks]