The width of a rectangle measures left bracket, 4, s, plus, 5, right bracket(4s+5) centimeters, and its length measures left bracket, 2, s, minus, 10, right bracket(2s−10) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
−5+6s
minus, 16, plus, 18, s−16+18s
12, s, minus, 1012s−10
9, s, minus, 89s−8
The perimeter of a rectangle is given by the sum of all its sides. For a rectangle, this is twice the width plus twice the length. If we denote the width as \( w \) and the length as \( l \), then the perimeter \( P \) is:
\[ P = 2w + 2l \]
Given that the width \( w \) is \( 4s + 5 \) and the length \( l \) is \( 2s - 10 \), we substitute these expressions into our formula:
\[ P = 2(4s + 5) + 2(2s - 10) \]
Now, we distribute the 2 into both parentheses:
\[ P = 2 \cdot 4s + 2 \cdot 5 + 2 \cdot 2s - 2 \cdot 10 \]
\[ P = 8s + 10 + 4s - 20 \]
Next, we combine like terms:
\[ P = 8s + 4s + 10 - 20 \]
\[ P = 12s - 10 \]
So the correct expression that represents the perimeter of the rectangle in centimeters is:
\[ 12s - 10 \]