Answer:
The length of each edge of the base is 7cm.
Step-by-step explanation:
The volume of a prism with square base is given by:
[tex]V = l^{2}h[/tex]
In which l is the length of each edge of the base and h is the height.
A prism with a square base has a height of 15cm and a volume of 735cm3.
This means that [tex]V = 735, h = 15[/tex]
So
[tex]V = l^{2}h[/tex]
[tex]735 = 15l^{2}[/tex]
[tex]l^{2} = \frac{735}{15}[/tex]
[tex]l^{2} = 49[/tex]
[tex]l = \pm \sqrt{49}[/tex]
Length is a positive measure. So
[tex]l = 7[/tex]
Volume in cm³, so the length of each edge is in cm.
The length of each edge of the base is 7cm.
