The width of a rectangle measures left parenthesis, 5, r, plus, 8, s, right parenthesis(5r+8s) centimeters, and its length measures left parenthesis, 7, r, minus, 7, s, right parenthesis(7r−7s) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Question
The width of a rectangle measures left parenthesis, 5, r, plus, 8, s, right parenthesis(5r+8s) centimeters, and its length measures left parenthesis, 7, r, minus, 7, s, right parenthesis(7r−7s) 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 (5r+8s) centimeters and its length is (7r−7s) centimeters, we can substitute these values into the formula.
So, the perimeter P of the rectangle is:
P = 2 * [(5r+8s) + (7r−7s)]
Simplify the expression inside the brackets:
P = 2 * [(5r + 7r) + (8s - 7s)]
P = 2 * [12r + s]
So, the expression that represents the perimeter of the rectangle in centimeters is 2 * [12r + s].
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