Question

Find the missing side.

Answer 1

This is one of the two tired triangles of trig; the isosceles right triangle, half a square, aka 45/45/90.  The other one is the 30/60/90 right triangle, half an equilateral triangle.  You will be tormented with these two baby triangles for much of your middle school and high school math life, and probably beyond that.  Learn the following facts, learn how to use these facts, and you will breeze through a lot of geometry, trigonometry, and even physics.

Here are the facts:

The ratio of the sides in the 30/60/90 triangle are 1:√3:2

The ratio of the sides in the 45/45/90 triangle are 1:1:√2

Easy.  Note the order; the smallest side is opposite the smallest angle, and they increase like you'd expect.

Here we have 45/45/90 so

x:y:14√2 = 1:1:√2

from which we obviously conclude  x=14, y=14

Answer: C)  x=14, y=14