The area of a rectangle is given by: 5x^2-22x + 8. What are the possible
dimensions of the rectangle?
To find the possible dimensions of the rectangle, we need to factor out the given expression, 5x^2-22x + 8, into two factors that represent the length and the width of the rectangle.
5x^2-22x + 8 can be factored into (5x-2)(x-4).
Therefore, the possible dimensions of the rectangle are (5x-2) by (x-4).
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To find the possible dimensions of the rectangle, we need to factorize the given expression for the area.
The area of a rectangle can be determined by multiplying its length and width.
Given: Area = 5x^2 - 22x + 8
To factorize the expression, we need to find two binomials that multiply together to give the expression.
The factors of 5x^2 are either 5x and x or x and 5x.
The factors of 8 are either 1 and 8 or 2 and 4.
We can set up different possibilities for the factors:
1. (5x + 1) and (x + 8)
2. (5x + 2) and (x + 4)
3. (x + 1) and (5x + 8)
4. (x + 2) and (5x + 4)
To check which set of factors is correct, we can multiply them together and see if we get the original expression.
1. (5x + 1)(x + 8) = 5x^2 + 41x + 8 (not equal to the given expression)
2. (5x + 2)(x + 4) = 5x^2 + 22x + 8 (equal to the given expression)
3. (x + 1)(5x + 8) = 5x^2 + 13x + 8 (not equal to the given expression)
4. (x + 2)(5x + 4) = 5x^2 + 14x + 8 (not equal to the given expression)
Therefore, the correct factorization is (5x + 2)(x + 4).
From this, we can determine the possible dimensions of the rectangle:
Length = 5x + 2
Width = x + 4
So, the possible dimensions of the rectangle are (5x + 2) and (x + 4).
To determine the possible dimensions of a rectangle given its area, we need to factor the equation 5x^2 - 22x + 8.
Step 1: Factor the expression
To factor the quadratic expression, we need to split the middle term (-22x) into two terms that, when multiplied together, give us the product of the first and last term. In this case, the product of the first and last term is (5x^2)(8) = 40x^2.
Let's find two numbers whose product is 40 and whose sum is -22.
The numbers are -20 and -2 because (-20) * (-2) = 40 and (-20) + (-2) = -22.
Now we can rewrite the quadratic expression by splitting the middle term:
5x^2 - 20x - 2x + 8
Step 2: Group the terms
Now we group the terms together:
(5x^2 - 20x) + (-2x + 8)
Step 3: Factor by grouping
Factor out the common factors from each group:
5x(x - 4) - 2(x - 4)
Step 4: Factor out the common binomial factor
Now we can factor out the common binomial factor (x - 4) from both terms:
(x - 4)(5x - 2)
Step 5: Set each factor equal to zero
Now set each factor equal to zero and solve for x:
x - 4 = 0 --> x = 4
5x - 2 = 0 --> 5x = 2 --> x = 2/5
The possible dimensions of the rectangle are x - 4 and 5x - 2, where x is either 4 or 2/5.
Therefore, the possible dimensions of the rectangle are 4 by 18, or 2/5 by 8/5.