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The width of a rectangle measures
(2.9 p-3.9) centimeters, and its length measures
(9.4 p-3.5) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

-14.8+24.6 p

-7.4+12.3 p

-p+5.9

-2p+11.8

The width of a rectangle measures $(2.9 p-3.9)$ centimeters, and its length measures $(9.4 p-3.5)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $-14.8+24.6 p$ $\newline$ $-7.4+12.3 p$ $\newline$ $-p+5.9$ $\newline$ $-2 p+11.8$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(2.9 p-3.9)

centimeters, and its length measures

(9.4 p-3.5)

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

\newline

-14.8+24.6 p

\newline

-7.4+12.3 p

\newline

-p+5.9

\newline

-2 p+11.8

Write Given Expressions: To find the perimeter of a rectangle, we use the formula $P = 2(l + w)$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width. Let's first write down the given expressions for the length and width. $\newline$ Length ( $l$ ) = $(9.4p - 3.5)$ cm $\newline$ Width ( $w$ ) = $(2.9p - 3.9)$ cm $\newline$ Now we will plug these expressions into the perimeter formula.
Combine Like Terms: The expression for the perimeter is $P = 2[(9.4p - 3.5) + (2.9p - 3.9)]$ . First, we add the expressions inside the brackets.
Multiply by $2$ : Inside the brackets, we combine like terms: $(9.4p + 2.9p)$ and $(-3.5 - 3.9)$ . This gives us $(12.3p)$ and $(-7.4)$ . So, inside the brackets we have $(12.3p - 7.4)$ .
Simplify Result: Now we multiply the entire expression inside the brackets by $2$ to find the perimeter. $\newline$ $P = 2 \times (12.3p - 7.4)$
Simplify Result: Now we multiply the entire expression inside the brackets by $2$ to find the perimeter. $\newline$ $P = 2 \times (12.3p - 7.4)$ Multiplying each term inside the brackets by $2$ gives us $P = 2 \times 12.3p - 2 \times 7.4$ . $\newline$ This simplifies to $P = 24.6p - 14.8$ .

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