Answer:
<em>Answer: C. 32 cm</em>
Step-by-step explanation:
<u>Triangle Inequality Theorem
</u>
Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:
x + y > z
x + z > y
y + z > x
Combining the above inequalities, and provided y>z, the third size must satisfy:
y - z < x < y + z
We know the triangle has two congruent angles, which means the triangle is isosceles, i.e., it has two congruent sides.
We are given two side lengths of 16 cm and 32 cm. The third side must have a length of 16 cm or 32 cm for the triangle to be isosceles.
If the third side had a length of 16 cm then the lengths would be 16-16-32. But that combination cannot form a triangle because of the condition stated above.
If y=16, z=16, and x=32 (the worst possible combination), then the inequality
0 < x < 32
wouldn't be satisfied, thus the third side cannot have a length of 16 cm and it must have a length of 32 cm
Answer: C. 32 cm
