Triangle Side Length and Ratios

Question

What is the perimeter of a basic 30-60-90  triangle (with side lengths equal to the ratio values)? What is the perimeter of a basic 45-45-90 triangle? What would the answers be in both estimated and simplified form?

What is the ratio of the 30-60-90 triangle’s perimeter to the 45-45-90 triangle’s perimeter? What are the steps to get this answer in both simplified and estimated form? Is this ratio true for all 30-60-90 and 45-45-90 triangles?

Answer 1

A 30-60-90 right triangle has sides in ratio of 1:radical 3:2 perimeter = 3 + radical 3

A 45-45-90 right triangle has sides in ratio of 1:1:radical 2 perimeter = 2 + radical 2

The ratio of those two perimeters is 3 + radical 3 / 2 + radical 2.

To convert so radical is not in the denominator, multiply top and bottom of fraction by 2 - radical 2.