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The width of a rectangle measures
(6.9 p-8.9 q) centimeters, and its length measures
(7.7 p-3.3 q) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

14.6 p-12.2

29.2 p-24.4

29.2 p-6.6 q-8.9

29.2 p-24.4 q

The width of a rectangle measures $(6.9 p-8.9 q)$ centimeters, and its length measures $(7.7 p-3.3 q)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $14.6 p-12.2$ $\newline$ $29.2 p-24.4$ $\newline$ $29.2 p-6.6 q-8.9$ $\newline$ $29.2 p-24.4 q$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(6.9 p-8.9 q)

centimeters, and its length measures

(7.7 p-3.3 q)

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

\newline

14.6 p-12.2

\newline

29.2 p-24.4

\newline

29.2 p-6.6 q-8.9

\newline

29.2 p-24.4 q

Perimeter Formula: To find the perimeter of a rectangle, we need to add up all the sides. The formula for the perimeter $P$ of a rectangle is $P = 2 \times (\text{length} + \text{width})$ .
Expressions for Length and Width: First, let's write down the expressions for the length and the width of the rectangle: $\newline$ Length $L = (7.7 p - 3.3 q)$ cm $\newline$ Width $W = (6.9 p - 8.9 q)$ cm
Add Length and Width: Now, we will add the length and the width expressions: $\newline$ $L + W = (7.7 p - 3.3 q) + (6.9 p - 8.9 q)$
Combine Like Terms: Combine like terms in the expression: $\newline$ $L + W = (7.7 p + 6.9 p) - (3.3 q + 8.9 q)$ $\newline$ $L + W = 14.6 p - 12.2 q$
Use Perimeter Formula: Now, we will use the perimeter formula and multiply the sum of length and width by $2$ : $\newline$ $P = 2 \times (L + W)$ $\newline$ $P = 2 \times (14.6 p - 12.2 q)$
Multiply by $2$ : Multiply each term inside the parentheses by $2$ : $\newline$ $P = 2 \times 14.6 p - 2 \times 12.2 q$ $\newline$ $P = 29.2 p - 24.4 q$

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