Consider the figure below.

What are the values of x and y?

Answers:

x = 14

y = 14

Explanation:

The tickmarks indicate the sides x and y are the same length.

So y = x or x = y

We can use the Pythagorean theorem to say

a^2 + b^2 = c^2

x^2 + y^2 = (14*sqrt(2))^2

x^2 + x^2 = 14^2*(sqrt(2))^2

2x^2 = 196*2

x^2 = 196   divide both sides by 2

x = sqrt(196)

x = 14

This must mean that y = 14 as well.

This triangle is an isosceles right triangle. We also consider it a 45-45-90 triangle because the three angles are 45, 45, and 90 degrees.

For any 45-45-90 triangle, the hypotenuse is always sqrt(2) times the leg length.

hypotenuse = leg*sqrt(2)