an aquarium holding african cichlids is 2 inches higher than it is wide. Its length is 29 inches and its volumne is 3480 cubic inches. what is the height and width inches.
length --- 29
width ---- x
height ----x+2
29x(x+2) = 3480
divide by 29 and expand
x^2 + 2x = 120
x^2 + 2x - 120 = 0
(x+12)(x-10) = 0
x = 10 or x is a negative, which can't be
the width is 10 inches
the height is 12 inches
check: 10(12)(29) = 3480
An aquarium holding african cichlids is 3inches higher than it is wide.Its length is 28inches,volume is 3640?
To find the height and width of the aquarium, we can set up equations based on the given information.
Let's assume the width of the aquarium is x inches.
Since the height is 2 inches higher than the width, the height can be expressed as (x + 2) inches.
The length of the aquarium is given as 29 inches.
The formula to calculate the volume of a rectangular prism is V = length × width × height. In this case, the volume is given as 3480 cubic inches, so we have:
3480 = 29 × x × (x + 2)
Now, we can solve this equation for x.
Expanding the equation:
3480 = 29x² + 58x
Rearranging the equation to make it a quadratic equation:
29x² + 58x - 3480 = 0
Next, we can factor this quadratic equation or use the quadratic formula to find the values of x. We will use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Here, a = 29, b = 58, and c = -3480.
Substituting these values into the quadratic formula:
x = (-58 ± √((58)² - 4(29)(-3480))) / (2(29))
After calculating, we get two possible values for x: x ≈ 12 and x ≈ -30.
Since the width cannot be negative, the width of the aquarium is approximately x = 12 inches.
To find the height, we can substitute this value back into the expression (x + 2):
height = x + 2 = 12 + 2 = 14 inches.
Therefore, the width of the aquarium is approximately 12 inches and the height is approximately 14 inches.
To find the height and width of the aquarium, we can set up a system of equations based on the given information.
Let's denote the width of the aquarium as x inches.
According to the problem, the height is 2 inches higher than the width, so the height of the aquarium can be represented as (x + 2) inches.
The length of the aquarium is given as 29 inches.
The volume of the aquarium is also given as 3480 cubic inches. The formula for the volume of a rectangular prism is length × width × height.
So, we have the equation:
29x(x + 2) = 3480
To solve this equation, we can start by simplifying it:
29x^2 + 58x = 3480
Next, let's rearrange the equation in standard quadratic form:
29x^2 + 58x - 3480 = 0
Now, we can solve this quadratic equation. There are different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
In this case, let's use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation 29x^2 + 58x - 3480 = 0, we have a = 29, b = 58, and c = -3480.
Substituting these values into the quadratic formula, we get:
x = (-58 ± √(58^2 - 4 * 29 * -3480)) / (2 * 29)
Now we can simplify and calculate the solutions for x:
x = (-58 ± √(3364 + 403680)) / 58
x = (-58 ± √406044) / 58
x = (-58 ± 638.02) / 58
Now we have two possible solutions for x:
x₁ = (-58 + 638.02) / 58 ≈ 10.76
x₂ = (-58 - 638.02) / 58 ≈ -11.03
Since the width cannot be negative, we disregard x₂ as an extraneous solution.
Therefore, the width of the aquarium is approximately 10.76 inches.
To find the height, we can substitute this value back into the equation for height:
height = x + 2 = 10.76 + 2 = 12.76 inches
So, the height of the aquarium is approximately 12.76 inches, and the width is approximately 10.76 inches.