An aquarium holding African cichlids is 2 inches higher than it is wide. Its length is 25 inches, and its volume is 9000 cubic inches. What is the height and width?
Volume = length(width)(height)
Now sub in what you know
9000 = 25(width)(height)
Now let x represent the width, so x + 2 is the height
now sub that in
9000= 25(x)(x+2)
solve for x : )
so solve for x and a tutor can check your work : )
To find the height and width of the aquarium, we can use the given information and the formula for the volume of a rectangular prism.
Let's assign variables to the height and width of the aquarium.
Let:
H = height
W = width
From the given information:
Length (L) = 25 inches
Volume (V) = 9000 cubic inches
The formula for the volume of a rectangular prism is: V = L × W × H
Substituting the given values into the formula, we have:
9000 = 25 × W × H
Now, observe the given information that the aquarium's height is 2 inches greater than its width. We can express this as:
H = W + 2
Substituting this expression into the equation above, we get:
9000 = 25 × W × (W + 2)
Simplifying the equation, we have:
9000 = 25W^2 + 50W
Rearranging the equation to make it easier to solve, we have:
25W^2 + 50W - 9000 = 0
This is now a quadratic equation in standard form. We can solve it by factoring, completing the square, or using the quadratic formula.
Let's solve it using factoring:
25W^2 + 50W - 9000 = 0
Divide both sides of the equation by 25 to simplify it:
W^2 + 2W - 360 = 0
Now, factor the left side of the equation:
(W + 20)(W - 18) = 0
Setting each factor equal to zero, we get two possible solutions for W:
W + 20 = 0 or W - 18 = 0
Solving these equations, we find two possible widths:
W = -20 or W = 18
Since width cannot be negative, we disregard W = -20, and we are left with the solution:
W = 18 inches
Now that we know the width, we can find the height (H) using the expression:
H = W + 2
H = 18 + 2
H = 20 inches
Therefore, the height of the aquarium is 20 inches and the width is 18 inches.