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The width of a rectangle measures
(5.7 n+8.8) centimeters, and its length measures
(6.1 n+3.6) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

9.7+14.5 n

19.4+29 n

12.4+11.8 n

24.8+23.6 n

The width of a rectangle measures $(5.7 n+8.8)$ centimeters, and its length measures $(6.1 n+3.6)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $9.7+14.5 n$ $\newline$ $19.4+29 n$ $\newline$ $12.4+11.8 n$ $\newline$ $24.8+23.6 n$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(5.7 n+8.8)

centimeters, and its length measures

(6.1 n+3.6)

centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

\newline

9.7+14.5 n

\newline

19.4+29 n

\newline

12.4+11.8 n

\newline

24.8+23.6 n

Identify Formula: Identify the formula for the perimeter of a rectangle. $\newline$ The perimeter $P$ of a rectangle is given by the formula $P = 2(\text{length} + \text{width})$ .
Substitute Expressions: Substitute the given expressions for length and width into the perimeter formula. $\newline$ $P = 2((6.1n + 3.6) + (5.7n + 8.8))$
Combine Like Terms: Combine like terms inside the parentheses. $\newline$ P = $2$ (($\(6\).\(1\)n + \(5\).\(7\)n) + (\(3\).\(6\) + \(8\).\(8\)))
Simplify Expression: Simplify the expression inside the parentheses. \(P = 2((11.8n) + (12.4))\)
Distribute \(2\): Distribute the \(2\) across the terms inside the parentheses.\[P = 2 \times 11.8n + 2 \times 12.4\]
Perform Multiplication: Perform the multiplication to find the perimeter expression.\(\newline\)\(P = 23.6n + 24.8\)

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