This problem involves a right triangle, and you're asked to find the hypotenuse. To solve it, we use the Pythagorean theorem, which states:

$c^2 = a^2 + b^2$

where:

• $c$ is the hypotenuse,
• $a$ and $b$ are the legs of the triangle.

Given:

• $a = 16$ cm,
• $b = 10$ cm.

Now we can calculate the hypotenuse:

$c = \sqrt{a^2 + b^2} = \sqrt{16^2 + 10^2}$

Let’s compute that.

$c = \sqrt{256 + 100} = \sqrt{356}$

$c \approx 18.9 \, \text{cm}$

So, the measure of the hypotenuse is approximately 18.9 cm, rounded to the nearest tenth.

Would you like more details on this calculation?

Here are 5 questions to expand your knowledge:

1. What is the Pythagorean theorem, and why does it work?
2. How can you verify if a triangle is a right triangle using side lengths?
3. What happens to the hypotenuse when the other legs are increased in length?
4. Can the Pythagorean theorem be used in non-right triangles?
5. How would the answer change if the legs were 3 times their original lengths?

Tip: Always make sure your units are consistent when applying the Pythagorean theorem to avoid errors.