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 ?
(x+3) / (3x-1) = 1/2
2 x + 6 = 3 x - 1
x = 7
GR = 3(7) - 1 = 20
SETW
20
Oh boy, let's solve this triangle trouble!
We're given that the ratio of Triangle BOY to Triangle GRL is 1:2. So if we have BO = x + 3, and GR = 3x - 1, we need to figure out the value of x to find the length of GR.
To find x, we can set up the ratio:
BOY / GRL = BO / GR
Substituting the given values, we get:
1/2 = (x + 3) / (3x - 1)
Now, we have a proportion problem, so let's cross-multiply:
2(x + 3) = 1(3x - 1)
Simplifying the left side:
2x + 6 = 3x - 1
Rearranging and combining like terms:
2x - 3x = -1 - 6
-x = -7
Dividing by -1:
x = 7
Great, we found the value of x! Now we can plug it back into GR = 3x - 1:
GR = 3(7) - 1
GR = 21 - 1
GR = 20
So the length of GR is 20. Voila!
To find the length of GR, we can set up a proportion of the ratios of the sides in similar triangles BOY and GRL.
The given ratio of similarity is 1:2, which means that the corresponding sides of the triangles are in the same ratio.
Let's set up the proportion:
BOY/ GRL = 1/2
Now, substitute the values for BO and GR:
(x + 3) / (3x - 1) = 1/2
To solve this proportion, we can cross-multiply:
2(x + 3) = 1(3x - 1)
2x + 6 = 3x - 1
Rearrange the equation to isolate the variable:
2x - 3x = -1 - 6
-x = -7
Now, multiply both sides by -1 to solve for x:
x = 7
Now that we have the value of x, we can substitute it back into the expression for GR:
GR = 3x - 1
GR = 3(7) - 1
GR = 21 - 1
GR = 20
Therefore, the length of GR is 20.