The volume of any prisma no matter wich one side it have got the following formula:
V=Ab*h where Ab is the base area and h is called height.
From our data we know the volume (6k^2-13K+5) and we know the base area (2k-1). Inserting this data in the general formula we got:
6k^2-13K+5=(2k-1)*h, solving for our unknown variable the height h
h=6k^2-13K+5/2k-1
factoring numerator :
h=(3k-5)(2k-1)/2k-1 simplifying
h=3k-5
The answer is 3k-5
Remark
The Volume = B * h
V = 6k^2 - 13k + 5
B = 2k - 1
h = ??
The volume will factor into (2k - 1)(3k - 5)
You can tell that one of the factors is 2k - 1 because that is the given amount for the base. You need only find the other factor. 3k is needed to multiply 2k to 6k^2.
- 1 needs - 5 to get the answer to 5
So the other factor is 3k - 5
Solution
V/b = h
(6k^2 - 13k + 5)/(2k - 1)
(3k - 5)(2k - 1) / (2k - 1) The (2k - 1)s Cancel out
Answer
B = 3k - 5 Second one down.
