The ratio of similarity of triangle BOY to triangle GRL is 1:2, if BO = x+3 and GR=3x-1, then the length of GR is

The length of GR is 20.

The ratio of BOY/GRL is 1/2. This gives us part of our proportion we will set up.

BO/GR = (x+3) / (3x-1); now our proportion is

(x+3) / (3x-1) = 1/2

Cross multiply:

2 (x+3) = 1 (3x-1)

Using the distributive property, we have

2*x + 2*3 = 1*3x - 1*1

2x + 6 = 3x - 1

Gathering all variables on one side, we subtract 2x:

2x + 6 - 2x = 3x - 1 - 2x

6 = x - 1

Adding 1 to both sides,

6+1 = x-1+1

7 = x

Since x=7, we substitute this into our expression for GR:

GR = 3x-1 = 3 (7) - 1 = 21 - 1 = 20