The width of a rectangle measures left parenthesis, 10, p, minus, 9, q, right parenthesis(10p−9q) centimeters, and its length measures left parenthesis, 7, p, plus, 8, q, right parenthesis(7p+8q) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Question
The width of a rectangle measures left parenthesis, 10, p, minus, 9, q, right parenthesis(10p−9q) centimeters, and its length measures left parenthesis, 7, p, plus, 8, q, right parenthesis(7p+8q) 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 (10p - 9q) centimeters and the length is (7p + 8q) centimeters, we can substitute these values into the formula.
So, the perimeter of the rectangle is 2 * [(10p - 9q) + (7p + 8q)].
Simplify the expression inside the brackets: (10p - 9q + 7p + 8q).
Combine like terms: (10p + 7p) + (-9q + 8q) = 17p - q.
So, the perimeter of the rectangle is 2 * (17p - q) = 34p - 2q centimeters.
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