The area of a rectangle is given by: 5x^2 -22x + 8. What are the possible dimensions of the rectangle?
Ah, the dimensions of a rectangle, the building blocks of many shapes! To find the possible dimensions of this rectangle, we need to factor the given polynomial. Let me put on my clown hat and give it a try.
So, the polynomial 5x^2 - 22x + 8 can be factored as (x - 2)(5x - 4). Now, in a rectangle, the length and width must be positive values, so we disregard any negative values of x.
So, the possible dimensions of the rectangle could be (x - 2) and (5x - 4), where x is greater than or equal to 2.
Keep in mind, these are just the possible dimensions. The actual dimensions of the rectangle will depend on the specific value of x that you substitute in. So, if you want to find the actual dimensions, you'll need to plug in a specific value for x and calculate.
Hope that helps, and remember, rectangles are like comedians - they come in all shapes and sizes!
To find the possible dimensions of the rectangle, we need to factor the given expression, 5x^2 - 22x + 8.
The expression can be factored as follows:
5x^2 - 22x + 8 = (x - 2)(5x - 4)
From this factored form, we can see that the possible dimensions of the rectangle are:
Length: x - 2
Width: 5x - 4
These dimensions will result in the given area of the rectangle.
To find the possible dimensions of a rectangle given its area expression, you need to factorize the given expression. The factored form will represent the dimensions of the rectangle.
Given the area expression: 5x^2 - 22x + 8
First, we need to find two numbers that when multiplied give +40 (the product of the coefficient of x^2, 5, and the constant term, 8) and when added, give -22 (the coefficient of x, -22).
The numbers that satisfy these two conditions are -2 and -20.
We can now factorize the expression using these two numbers:
5x^2 - 22x + 8 = (5x - 2)(x - 4)
The factored form (5x - 2)(x - 4) represents the dimensions of the rectangle. Therefore, the possible dimensions of the rectangle are (5x - 2) and (x - 4).
A = L ∙ W = 5 x² - 22 x + 8
For any quadratic equation:
a x² - b x + c = a ( x - x₁ ) ( x - x₂ )
where x₁ = x₂ are roots of that quadratic equation.
In this case:
5 x² - 22 x + 8 = 0
a = 5 , b = - 22 , c = 8
The solutions are:
2 / 5 and 4
So
5 x² - 22 x + 8 = 5 ( x - 2 / 5 ) ( x - 4 )
Possible dimensions are:
L = 5 ( x - 2 / 5 ) , W = x - 4
L = 5 x - 2 , W = x - 4
and
L = x - 2 / 5 , W = 5 ( x - 4 )
L = x - 2 / 5 , W = 5 x - 20