Question

Which of the following combination of sides of a triangle represents a right angled triangle?

• A. 4 cm, 6 cm and 8 cm
• B. 8 cm, 12 cm and 16 cm
• C. 5 cm, 9 cm and 10 cm
• D. 9 cm, 12 cm and 15 cm

Answer 1

The correct option is D

9 cm, 12 cm and 15 cm

In a right angled triangle, the hypotenuse is the largest side.
If XY is the largest side of a triangle XYZ, then${\left(XY\right)}^2$= ${\left(XZ\right)}^2+{\left(YZ\right)}^2$. Thus, XYZ is a right angled triangle with XY as hypotenuse and angle XZY equal to ${90}^0$.
If${\left(XY\right)}^2>{\left(XZ\right)}^2+{\left(YZ\right)}^2$ then, XYZ is an obtuse angled triangle with angle XZY greater than ${90}^0$ and if ${\left(XY\right)}^2<{\left(XZ\right)}^2+{\left(YZ\right)}^2$ then, XYZ is an acute angled triangle with angle XZY less than ${90}^0$ .

Option D is a right angled triangle as ${\left(15\right)}^2={\left(9\right)}^2+{\left(12\right)}^2$or 225 = 81 + 144, whereas Option A and B are obtuse angled triangles and Option C is an acute angled triangle.