Question

If two sides of a triangle measure 30 and 60, which of the following cannot be the measure of the third side?

(A) 30

(B) 31

(C) 40

(D) 60

Short answer

(B) 31 cannot be the measure of the third side.

Step-by-step solution

Step 1. Concept of triangles and its properties

A triangle has three sides, three angles and three vertices. The sum of all internal angles of a triangle is always equal to${180}^{\circ }.$The sum of length of two sides of a triangle is greater than the length of third side.

Step 2. Measurements of triangle side

The ratio of the sines of each angle divided by the length of the opposite side is all equal. This helps you to find the sides of the triangle. Add the two angles together and subtract the sum from 180 degrees to find the third angle.

Step 3. Justification for the answer

From the above description, we can see that 31 cannot be the measure of third side.