the length of a rectangle is x inches and its width is 4 inches more than two thirds of its length. What is the perimeter of the rectangle in inches?
I am so lost, please help. The length of a rectangle is x inches and its width is 4 inches more than two thirds of its length. What is the perimeter of the rectangle in inches?
2L + 2W = P
If L = x, then W = 2/3x + 4
2x + 2(2/3x+4) = P
2x + 4/3x + 8 = P
Combine like terms.
To find the perimeter of a rectangle, we need to add up all four sides. In this case, we know that the length of the rectangle is x inches.
The width of the rectangle is given as "4 inches more than two thirds of its length." Let's break this down.
Two-thirds of the length of the rectangle is (2/3) * x inches.
Adding 4 inches to two-thirds of the length gives (2/3) * x + 4 inches.
So the width of the rectangle is (2/3) * x + 4 inches.
To find the perimeter, we need to add up all four sides:
Perimeter = 2 * (Length + Width)
Substituting the values we have:
Perimeter = 2 * (x + (2/3) * x + 4)
Simplifying:
Perimeter = 2 * (x + (2/3) * x + 4)
= 2 * (5/3 * x + 4)
= 10/3 * x + 8
Therefore, the perimeter of the rectangle is given by the expression 10/3 * x + 8 inches.