The width of a rectangle measures left parenthesis, 9, v, minus, 5, w, right parenthesis(9v−5w) centimeters, and its length measures left parenthesis, 9, v, plus, 6, w, right parenthesis(9v+6w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Question
The width of a rectangle measures left parenthesis, 9, v, minus, 5, w, right parenthesis(9v−5w) centimeters, and its length measures left parenthesis, 9, v, plus, 6, w, right parenthesis(9v+6w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Solution
The perimeter of a rectangle is given by the formula 2*(length + width).
Given that the width of the rectangle is (9v - 5w) centimeters and the length is (9v + 6w) centimeters, we can substitute these values into the formula.
So, the perimeter P of the rectangle is:
P = 2 * [(9v - 5w) + (9v + 6w)]
Simplify the expression inside the brackets:
P = 2 * [9v - 5w + 9v + 6w]
Combine like terms:
P = 2 * [18v + w]
So, the expression that represents the perimeter of the rectangle in centimeters is 2 * (18v + w).
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