Question

If a triangle has lengths of 45 cm and 9 cm, check all the possible lengths for the third side: 39 cm, 54 cm, 58 cm, 35 cm, 47 cm.

Answer 1

Using the triangle inequality theorem, the possible lengths for the third side of a triangle with sides of 45 cm and 9 cm are 39 cm, 35 cm, and 47 cm.

Step-by-step explanation:

To determine the

possible lengths

for the third side of a triangle when two sides are given as 45 cm and 9 cm, 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. Thus, for each option:

• 39 cm: 45 + 9 > 39 and 45 + 39 > 9 and 9 + 39 > 45, so it is possible.
• 54 cm: 45 + 9 > 54 does not hold, so it is not possible.
• 58 cm: 45 + 9 > 58 does not hold, so it is not possible.
• 35 cm: 45 + 9 > 35 and 45 + 35 > 9 and 9 + 35 > 45, so it is possible.
• 47 cm: 45 + 9 > 47 and 45 + 47 > 9 and 9 + 47 > 45, so it is possible.

The

possible lengths

for the third side are 39 cm, 35 cm, and 47 cm.