Question

The radius of this circle is one unit.

Find the exact lengths of the legs in the right triangle if:

Sides a is twice as long as side b.

And Sides b is twice as long as side a.

Basically the hypotenuse of this triangle is 1 and we are trying to use the pythagorean theorem to find the lengths of side a and b according to the terms described above.

Answer 1

if b=2a, then

a^2 + (2a)^2 = 1
5a^2 = 1
a = 1/√5

similarly for a=2b

Answer 2

first case 1: a = 2b

so a^2 + b^2 = 1^2
(2b)^2 + b^2 = 1
5b^2 = 1
b^2 = 1/5
b = 1/√5
one side is 1/√5, the other is 2/√5

you do case 2