The length of A, B, C are in the ratio 2:5:3. If the length of c is 9bmetres, find the length of A and B
I'm pretty sure that there was just a typo.
"9bmeters" should probably be just "9 meters"
2:5:3 = 6:15:9
I mean, after all, how can 3x be 9 times as big as 5x?
Your math is so wrong.
Apologies for the confusion in my previous response. You are correct.
If the length of C is 9 meters and the ratio of A, B, and C is 6:15:9, we can find the value of x by setting up the equation:
3x = 9
Dividing both sides by 3, we find:
x = 3
So, the length of A is 6x = 6 * 3 = 18 meters.
The length of B is 15x = 15 * 3 = 45 meters.
Let's represent the length of A, B, C as A', B', and C', respectively.
Given that the ratio of A': B': C' is 2:5:3, we can express this relationship as:
A' : B' : C' = 2 : 5 : 3
Now, we're given that the length of C' (C) is 9 times the length of B' (B). Therefore:
C' = 9B'
Since B' represents B, we can rewrite the equation as:
C = 9B
Using the ratio A' : B' : C' = 2 : 5 : 3, we can substitute the value of C' from the equation above:
2 : 5 : 3 = A' : B' : 9B'
To simplify the ratio, we can divide each term by 2:
1 : 2.5 : 1.5 = A' : B' : 4.5B'
To make it easier to work with, let's multiply each term by 2:
2 : 5 : 3 = 2A' : 5B' : 9B'
Now we can see that the ratio of A : B : C is:
2A' : 5B' : 9B'
Comparing this with our equation C = 9B, we can see that:
C = 9B'
Thus, we can rewrite the ratio as:
2A' : 5B' : C
Replacing C with 9B, we have:
2A' : 5B' : 9B
Since A' represents A, we can replace A' with A:
2A : 5B' : 9B
And since B' represents B, we can replace B' with B:
2A : 5B : 9B
Now we have the ratio of A : B : C:
2A : 5B : 9B
Therefore, the ratio of A to B is 2:5.
Let's assume the length of A is 2x, B is 5x, and C is 3x. Since the length of C is 9 times the length of B, we have:
3x = 9 * 5x
3x = 45x
Dividing both sides by 3:
x = 15
Therefore, the length of A is 2x = 2 * 15 = 30 meters.
The length of B is 5x = 5 * 15 = 75 meters.