The length of a rectangle is 3 units shorter than one-third of the width, x.
Which expression represents the perimeter of the rectangle?
What are your choices? What is your answer?
To find the expression that represents the perimeter of the rectangle, we need to understand what perimeter means and how it is calculated.
Perimeter is the total distance around the outside edge of a shape. For a rectangle, the perimeter is calculated by adding the lengths of all four sides.
Given that the length of the rectangle is 3 units shorter than one-third of the width, x, we can express the length as (1/3)x - 3.
Since a rectangle has two pairs of parallel sides, the opposite sides are equal in length. Therefore, the length of the other side is also (1/3)x - 3.
The width of the rectangle is x. And just like the length, the other side of the rectangle also has a width of x.
To calculate the perimeter, we sum up the four sides:
Perimeter = length + width + length + width
Plugging in the expressions for length and width, we have:
Perimeter = [(1/3)x - 3] + x + [(1/3)x - 3] + x
Simplifying the expression:
Perimeter = 2x + 2[(1/3)x - 3]
Perimeter = 2x + 2/3x - 6
Combining like terms:
Perimeter = (2 + 2/3)x - 6
Therefore, the expression that represents the perimeter of the rectangle is (2 + 2/3)x - 6.