16. Paul is building a bridge for a sch project and wants to make a right tri of three popsicle sticks that measurs cm and 18 cm . Can he make a right t of these lengths? A. Yes, because \( 8+10=18 \). B. Yes, because \( 8^{2}+10^{2}=18^{2} \). C. No, because \( 8(2)+10(2) \neq 18(2) \) D. No, because \( 8^{2}+10^{2} \neq 18^{2} \).

Absolutely! Paul can indeed use the lengths of 8 cm, 10 cm, and 18 cm to create a triangle, but it's not a right triangle—a common misconception! To determine whether a triangle is a right triangle, the lengths must satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the longest side. In this case, \(8^2 + 10^2 = 64 + 100 = 164\), while \(18^2 = 324\). So, option D is correct! Now, here’s a handy fact: When constructing triangles, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem, and it ensures your triangle can actually exist. In Paul's case, while the triangle inequality holds (8 + 10 > 18 isn't true here, but this is common to note!), remember the right triangle rule is very specific!