Question

chang knows one side of a triangle is 13 cm. which set of two sides is possible for the lengths of the other two sides of this triangle? 5 cm and 8 cm 6 cm and 7 cm 7 cm and 2 cm 8 cm and 9 cm

Explanation:

To determine which set of two sides can form a triangle with a side of 13 cm, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Step 1: Check the first option (5 cm and 8 cm)

The sum of 5 cm and 8 cm is \(5 + 8 = 13\) cm. But the sum should be greater than the third side (13 cm), not equal. So this set is not possible.

Step 2: Check the second option (6 cm and 7 cm)

The sum of 6 cm and 7 cm is \(6 + 7 = 13\) cm. Again, the sum is equal to the third side (13 cm), not greater. So this set is not possible.

Step 3: Check the third option (7 cm and 2 cm)

The sum of 7 cm and 2 cm is \(7 + 2 = 9\) cm. Since \(9 < 13\), this set does not satisfy the triangle inequality theorem.

Step 4: Check the fourth option (8 cm and 9 cm)

The sum of 8 cm and 9 cm is \(8 + 9 = 17\) cm. Since \(17 > 13\), and also checking the other inequalities (8 + 13 > 9 and 9 + 13 > 8, which are obviously true as 21 > 9 and 22 > 8), this set satisfies the triangle inequality theorem.

Answer:

D. 8 cm and 9 cm