A brick making company manufactures bricks with the same height and width. the volume of each brick is 108 cubic inches and the base area of each brick is 36 square inches. If the length of a brick is denoted as x and the height and width of the brick is denoted by y, find the dimensions of the brick.

the dimensions are x,y,3

To find the dimensions of the brick, we need to determine the value of x and y.

Given that the volume of each brick is 108 cubic inches and the base area is 36 square inches, we can use these two pieces of information to set up equations.

The volume of a rectangular solid is given by the formula:
Volume = length * width * height

From the problem statement, we know that the volume of each brick is 108 cubic inches:
108 = x * y * y

The base area of a rectangle is given by the formula:
Base Area = length * width

We are told that the base area of each brick is 36 square inches:
36 = x * y

Now, we have two equations with two variables. We can use substitution or elimination method to solve for x and y. Let's use the substitution method to solve this system of equations.

We have:
x * y * y = 108 (Equation 1)
x * y = 36 (Equation 2)

Rearrange Equation 2 to solve for x in terms of y:
x = 36 / y

Substitute this value of x into Equation 1:
(36 / y) * y * y = 108

Simplify the equation:
36 * y^2 = 108

Divide both sides by 36:
y^2 = 108 / 36

Simplify further:
y^2 = 3

Taking the square root of both sides, we get:
y = √3

Now, substitute this value of y back into Equation 2 to solve for x:
x * √3 = 36

Simplify:
x = 36 / √3

To rationalize the denominator, multiply the numerator and denominator by √3:
x = (36 * √3) / (√3 * √3)
x = (36 * √3) / 3
x = 12 * √3

Therefore, the dimensions of the brick are:
Length (x) = 12 * √3
Height and Width (y) = √3