Answer:
r = 3, h = 6
r = 6, h = 3
Explanation:
First, you need to use the first equation to solve for one variable in terms of the other.
R + h = 9
R = 9 - h
Then, you can substitute this expression for R into the second equation:
2 × r × h = 54
2 × (9 - h) × h = 54
Simplifying:
18h - 2h^2 = 54
2h^2 - 18h + 54 = 0
This is a quadratic equation, which you can solve using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in a = 2, b = -18, and c = 54, you get:
h = (18 ± sqrt(18^2 - 4(2)(54))) / (2(2))
h = (18 ± 6) / 4
h = 6 or h = 3
Now that you have values for h, you can use the first equation to solve for R:
R + h = 9
If h = 6, then R = 9 - h = 3
If h = 3, then R = 9 - h = 6
Therefore, the possible values for r and h are:
r = 3, h = 6
r = 6, h = 3