Two sides of a triangle measure 7 cm and 15 cm. Which could be the measure of the third side of the triangle?

To find the possible measure of the third side of a triangle when two sides are given, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let the two sides be (a = 7) cm and (b = 15) cm. We’ll analyze each option for the third side (c):

1. For (c = 7) cm:

– (7 + 7 > 15) (False)

– Not valid.

2. For (c = 22) cm:

– (7 + 15 > 22) (False)

– Not valid.

3. For (c = 18) cm:

– (7 + 15 > 18) (True)

– (7 + 18 > 15) (True)

– (15 + 18 > 7) (True)

– Valid option.

4. For (c = 25) cm:

– (7 + 15 > 25) (False)

– Not valid.

The only possible measure for the third side of the triangle is 18 cm.