The length of a rectangle is represented by 2x + 3 and the width by 2x -1. Find the perimeter as a polynomial in simplest form.
P = 2 L + 2 W
P = 2 ( 2 x + 3 ) + 2 ( 2 x - 1 )
P = 4 x + 6 + 4 x - 2
P = 8 x + 4
P = 4 ∙ 2 x + 4
P = 4 ( 2 x + 1 )
OR
P = 2 ( L + W )
P = 2 ( 2 x + 3 + 2 x - 1 )
P = 2 ( 4 x + 2 )
P = 2 [ 2 ( 2 x + 1 ) ]
P = 2 ∙ 2 ∙ ( 2 x + 1 )
P = 4 ( 2 x + 1 )
To find the perimeter of a rectangle, we add up the lengths of all four sides. In this case, we have the length represented by 2x + 3 and the width represented by 2x - 1.
The formula for the perimeter P of a rectangle is: P = 2(length + width).
Substituting the given expressions for length and width into the formula, we have:
P = 2(2x + 3 + 2x - 1)
Simplifying inside the parentheses:
P = 2(4x + 2)
Now, using the distributive property, we can multiply 2 by each term inside the parentheses:
P = 8x + 4
So, the perimeter of this rectangle, expressed as a polynomial in simplest form, is 8x + 4.