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The width of a rectangle measures
(9p+8q) centimeters, and its length measures
(7p-4q) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

4+16 p

8-8q+32 p

32 p+8q

32 p+8

The width of a rectangle measures $(9 p+8 q)$ centimeters, and its length measures $(7 p-4 q)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $4+16 p$ $\newline$ $8-8 q+32 p$ $\newline$ $32 p+8 q$ $\newline$ $32 p+8$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(9 p+8 q)

centimeters, and its length measures

(7 p-4 q)

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

\newline

4+16 p

\newline

8-8 q+32 p

\newline

32 p+8 q

\newline

32 p+8

Perimeter Formula: To find the perimeter of a rectangle, we need to add up the lengths of all four sides. The formula for the perimeter $P$ of a rectangle is $P = 2 \times (\text{length} + \text{width})$ .
Identify Length and Width: First, let's identify the length and width of the rectangle. The length is given as $7p-4q$ centimeters, and the width is given as $9p+8q$ centimeters.
Plug into Formula: Now, we will plug these expressions into the perimeter formula: $P = 2 \times ((7p-4q) + (9p+8q))$ .
Simplify Expression: Next, we simplify the expression inside the parentheses: $7p-4q$ + $9p+8q$ = $7p + 9p - 4q + 8q$ = $16p + 4q$ .
Find Perimeter: Now, we multiply this sum by $2$ to find the perimeter: $P = 2 \times (16p + 4q) = 32p + 8q$ .

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