The width of a rectangle measures left bracket, 7, r, minus, 2, s, right bracket(7r−2s) centimeters, and its length measures left bracket, r, minus, 5, s, right bracket(r−5s) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Question

The width of a rectangle measures left bracket, 7, r, minus, 2, s, right bracket(7r−2s) centimeters, and its length measures left bracket, r, minus, 5, s, right bracket(r−5s) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answer 1

The perimeter (P) of a rectangle is calculated by adding up all four sides. For a rectangle with a length (L) and a width (W), the perimeter formula is:

P = 2L + 2W

Given that the width (W) of the rectangle is (7r − 2s) centimeters and the length (L) is (r − 5s) centimeters, we can substitute these expressions into the perimeter formula:

P = 2(r − 5s) + 2(7r − 2s)

Now, distribute the 2 into each term inside the parentheses:

P = 2 * r - 2 * 5s + 2 * 7r - 2 * 2s
P = 2r - 10s + 14r - 4s

Now, combine like terms (the rs and the ss):

P = (2r + 14r) - (10s + 4s)
P = 16r - 14s

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

P = 16r - 14s