Find the sides of a rectangular prism if the volume = 30 cm^3 , the height = 3 cm and the perimeter of the base = 14 cm.

Volume of a rectangular prism is given by the
formula:

Volume = (Area of the rectangular cross
section)*Height

substituting given values of height and
volume in the above formula:

30 = (Area of the rectangular
cross
section)*3

Therefore:

Area of
the rectangular cross section = 30/3 = 10 cm^2

Let lengths
of two side of the triangle be x and
y

Then:

Area of rectangle =
x*y = 10

Therefore:

y =
10/x

And:

Perimeter of the
rectangle = 2*(x + y) = 14

==> x + y =
7

Substituting values of y as 10/x in above
equation:

x + 10/x =
7

Multiplying both sides by x, and shifting all the terms
of equation on left hand side:

x^2 - 7x + 10 =
0

==> x^2 - 2x - 5x + 10 =
0

==> x(x - 2) - 5(x - 2) =
0

==> (x - 2)(x - 5) =
0

Therefore:

x = 2 or
5

Therefore sides of the rectangular prism are 2 cm and 5
cm.