How are the proofs for the side length ratios of 30-60-90 and 45-45-90 triangles similar? how are they different?

As the ratios are different hence the two triangles are not similar.

Step-by-step explanation:

The side lengths ratios of one triangle are given as:

30-60-90

i.e. the sides are of length: 30x,60x,90x for some real number 'x'

and the side length ratio of the other triangle is given as:

45-45-90

i.e. the sides of the second triangle is given by:

45y,45y,90y for some real number 'y'.

" If all the sides of a triangle are proportional to the corresponding sides of another triangle then the triangles are said to be similar "

Now we check the ratio as:

As the 3 ratios are not equal hence the two triangles are not similar.

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)