Question

Select the condition for which it is NOT possible to construct a triangle.

A triangle with side lengths 4 cm, 5 cm, and 6 cm
A triangle with side lengths 4 cm, 5 cm, and 15 cm
A triangle with side lengths 4 cm and 5 cm and an included 50° angle
A triangle with angle measures 30° and 60°, and an included 3 cm side length.

Answer 1

B. A triangle with side lengths 4 cm, 5 cm, and 15 cm

Explanation:

A triangle is a three sided figure which also has three angles. It can be classified either according to its sides or according to the values of its angles.

Construction of a triangle involves having the dimensions of either two sides and included angle, three sides, or three angles, etc. With given dimensions, a triangle can be constructed appropriately.

In the given options, having a triangle with one side equals 15 cm would not form a complete shape with other sides of 4 cm and 5 cm. With these given dimensions, it is not possible to construct a triangle.

Answer 2

B. A triangle with side lengths 4 cm, 5 cm, and 15 cm

Explanation:

The addition of two of the sides of the triangle must be greater than the other side of the triangle. Sides of lengths 4 cm, 5 cm, and 15 don't make a triangle, because:

4 cm + 15 cm > 5 cm

5 cm + 15 cm > 4 cm

4 cm + 5 cm < 15 cm