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 8 cm

Answer 1

The possible sets of two sides for the lengths of the other two sides of the triangle are: 5 cm and 8 cm, 6 cm and 7 cm, and 8 cm and 8 cm.

Step-by-step explanation:

To determine which set of two sides is possible for the lengths of the other two sides of the triangle, we can use the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if one side of the triangle is 13 cm, then the sum of the other two sides must be greater than 13 cm in order for the triangle to be valid.

Let's check each set of two sides:

1. 5 cm and 8 cm: The sum of these two sides is 13 cm, which is equal to the given side. Therefore, this set of sides is possible.
2. 6 cm and 7 cm: The sum of these two sides is 13 cm, which is equal to the given side. Therefore, this set of sides is possible.
3. 7 cm and 2 cm: The sum of these two sides is 9 cm, which is less than the given side. Therefore, this set of sides is not possible.
4. 8 cm and 8 cm: The sum of these two sides is 16 cm, which is greater than the given side. Therefore, this set of sides is possible.

Based on the Triangle Inequality Theorem, the sets of two sides that are possible are: 5 cm and 8 cm, 6 cm and 7 cm, and 8 cm and 8 cm.

Answer 2

For triangle to be possible to draw there is one condition that it needs to suit.
The condition is:
largest side has to be shorter than sum of others 2.

in first case is:
13 = 8+5 which is equal but not greater than 13.

Last case:
13 < 8+8 which means that remaining lenghts are

8 and 8