Angles question

Question

A 30-60-90 degree triangle has side lengths with the ratio 1:2:\sqrt3. A $\footnotesize{45-45-90 degree triangle has side lengths with the ratio 1:1:\sqrt2.

a. What is the perimeter of a basic 30-60-90 degree triangle (with side lengths equal to the ratio values)? What is the perimeter of a basic 45-45-90 degree triangle? Write your answers in both simplified and estimated form.
b. What is the ratio of the 30-60-90 degrees triangle’s perimeter to the 45-45-90 degree triangle’s perimeter? Show how you arrived at your answer, and write your answer in both simplified and estimated form. Is this ratio true for all 30-60-90 degree and 45-45-90 degree

Answer 1

a.

Type A: perimeter of 30/60/90 triangle having hypotenuse 2 is 3+√3.

Type B: perimeter of 45/45/90 triangle having legs congruent of length 1 is 2+√2.

 

b.

Since there are infinitely many triangles of each of these two types, it makes little sense to compute a ratio of any one of type A to any other of type B.

 

(That is, are we taking a 'little'  30/60/90 triangle and a 'giant' 45/45/90 triangle?