The length of three line segments are a,b, and c respectively,
and a=2/3b c=3/2b then a : c = ?
a=2/3b
3a = 2b
b = 3a/2
c=3/2b
2c = 3b
b = 2c/3
thus: 2c/3 = 3a/2
4c = 9a
4/9 = a/c
a : c = 4 : 9
notice 2/3b ≠ 2/(3b)
I assumed you meant it the way you typed it.
a:b = 2:3
c:b = 3:2
we want b in the middle, so
b:c = 2:3
lcm(2,3) = 6, so now we can write
a:b = 4:6
b:c = 6:9
a:b:c = 4:6:9
a:c = 4:9
can you explain to me what you mean when you said you need "b" in the middle? thanks
b is bigger than a and smaller than c
it's not that b is the middle value, but that if we want to build a set of ratios,
a:b:c
we need to have a common value for b in the two ratios
a:b and b:c
We could not have placed a or c in the center spot, because we only had one ratio for each of those. But to join the two ratios, we need a single value for b.
To find the ratio between a and c, we need to compare their values.
Given that a = (2/3)b and c = (3/2)b, we can substitute these values into the ratio formula:
a : c = (2/3)b : (3/2)b
Next, we simplify the ratio by canceling out the common factor of b:
a : c = (2/3) : (3/2)
To simplify further, we can multiply the numerators and the denominators of the ratio by 2:
a : c = (2/3)*(2/2) : (3/2)*(2/2)
Simplifying yields:
a : c = 4/6 : 6/4
Now, we can reduce the fractions by dividing the numerator and the denominator of each fraction by their greatest common divisor, which in this case is 2:
a : c = (4/2)/(6/2) : (6/2)/(4/2)
Simplifying further, we get:
a : c = 2/3 : 3/2
Therefore, the ratio between a and c is 2/3 : 3/2.