1990 - 23 & 24

This new set is from the 1990 test.

Difficulty: Easy if you've got a good imagination ...

Difficulty: Medium. I like how this seems to not have enough information but when you model it algebraically, BOOM ...

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 21, answer 22, Published 5/17.