Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm

• Geometry

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer then how many such triangles exist?

1. 5
2. 10
3. 15
4. 21

Answer

If two sides are 8 and 15, then third side will have to be between (15-8) = 7 and (15+8) = 23.

When c is the longest side in obtuse triangle,

a² + b² < c²

If 15 is the longest side, then x can be 8, 9, 10, 11 or 12

If x is the longest side, then x can be 18, 19, 20, 21 or 22

Thus, 10 values of x are possible.

The correct option is B.