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The width of a rectangle measures
(3.6 q-3.4) centimeters, and its length measures
(2.1 q-6.8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

5.7 q-10.2

-4.7+0.2 q

11.4 q-20.4

-9.4+0.4 q

The width of a rectangle measures $(3.6 q-3.4)$ centimeters, and its length measures $(2.1 q-6.8)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $5.7 q-10.2$ $\newline$ $-4.7+0.2 q$ $\newline$ $11.4 q-20.4$ $\newline$ $-9.4+0.4 q$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(3.6 q-3.4)

centimeters, and its length measures

(2.1 q-6.8)

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

\newline

5.7 q-10.2

\newline

-4.7+0.2 q

\newline

11.4 q-20.4

\newline

-9.4+0.4 q

Perimeter Formula: To find the perimeter of a rectangle, we need to add together the lengths of all four sides. The formula for the perimeter $P$ of a rectangle is $P = 2 \times (\text{width} + \text{length})$ .
Calculate Sum: First, we calculate the sum of the width and the length: \(3. $6$ q - $3$ . $4$ ) + ( $2$ . $1$ q - $6$ . $8$ )\.
Combine Like Terms: Perform the addition by combining like terms: $3.6q + 2.1q = 5.7q$ and $-3.4 - 6.8 = -10.2$ . So, the sum of the width and the length is $5.7q - 10.2$ .
Apply Perimeter Formula: Now, we apply the perimeter formula: $P = 2 \times (5.7q - 10.2)$ .
Multiply Terms by $2$ : Multiply each term inside the parentheses by $2$ : $2 \times 5.7q = 11.4q$ and $2 \times -10.2 = -20.4$ .
Combine Results: Combine the results to get the expression for the perimeter: $11.4q - 20.4$ .

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