The width of a rectangle measures left bracket, 8, u, minus, 2, v, right bracket(8u−2v) centimeters, and its length measures left bracket, 5, u, plus, 9, v, right bracket(5u+9v) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Question

The width of a rectangle measures left bracket, 8, u, minus, 2, v, right bracket(8u−2v) centimeters, and its length measures left bracket, 5, u, plus, 9, v, right bracket(5u+9v) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answer 1

The perimeter (P) of a rectangle is the sum of all its sides. Since a rectangle has two lengths (l) and two widths (w), the perimeter can be calculated by the formula:

P = 2l + 2w

Given that the width (w) of the rectangle is (8u - 2v) centimeters and the length (l) is (5u + 9v) centimeters, we can plug these values into the perimeter formula:

P = 2(5u + 9v) + 2(8u - 2v)

Now we'll distribute the 2 into each term inside the parentheses:

P = 2 * 5u + 2 * 9v + 2 * 8u - 2 * 2v
P = 10u + 18v + 16u - 4v

Now, combine like terms:

P = (10u + 16u) + (18v - 4v)
P = 26u + 14v

Therefore, the expression that represents the perimeter of the rectangle, in centimeters, is:

P = 26u + 14v