What is the extended ratio relating the side lengths of a 45-45-90 triangle?

Question and answers are in the attached picture. you so much in advance.

The function models the number of accidents

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?