The area of a rectangle is 6n(to the power of 2) + n - 2. What is the expression that represents the perimeter of the rectangle?
area= LW=6n^2+n-2=(3n-2)(n+1)
perimeter then is 2L+2W=2(l+w)=2(3n-2+n+1)
= 2(4n-1)
To find the expression that represents the perimeter of the rectangle, we need to understand that the perimeter is the sum of all four sides of the rectangle.
A rectangle has two pairs of equal sides. Let's label the length of one pair of opposite sides as "L" and the width of the other pair of opposite sides as "W".
The formula for the perimeter of a rectangle is:
Perimeter = 2L + 2W
Given that the area of the rectangle is 6n^2 + n - 2, we need to first determine the length and width of the rectangle.
The area of a rectangle is calculated by multiplying the length by the width. So we need to find two factors that, when multiplied together, give us 6n^2 + n - 2.
To express 6n^2 + n - 2 as a product of two factors, we can attempt to factorize it:
6n^2 + n - 2 = (2n - 1)(3n + 2)
Now we have the factors of the area: (2n - 1) and (3n + 2).
The length of the rectangle (L) is represented by (3n + 2), and the width (W) is represented by (2n - 1).
Substituting these values into the formula for the perimeter, we get:
Perimeter = 2(3n + 2) + 2(2n - 1)
Simplifying the expression further:
Perimeter = 6n + 4 + 4n - 2
Combining like terms, we have:
Perimeter = 10n + 2
Therefore, the expression that represents the perimeter of the rectangle is 10n + 2.