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The width of a rectangle measures
(10 g-7) centimeters, and its length measures
(g-9) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

3g-8

-32+22 g

6g-16

11 g-16

The width of a rectangle measures $(10 g-7)$ centimeters, and its length measures $(g-9)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $3 g-8$ $\newline$ $-32+22 g$ $\newline$ $6 g-16$ $\newline$ $11 g-16$

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Find the magnitude of a vector

Full solution

Q. The width of a rectangle measures

(10 g-7)

centimeters, and its length measures

(g-9)

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

\newline

3 g-8

\newline

-32+22 g

\newline

6 g-16

\newline

11 g-16

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 $P = 2 \times (\text{width} + \text{length})$ .
Substitute Given Expressions: First, let's substitute the given expressions for the width and length into the perimeter formula: $\newline$ $P = 2 \times ((10g - 7) + (g - 9))$
Simplify Inside Parentheses: Now, we simplify the expression inside the parentheses: $\newline$ $(10g - 7) + (g - 9) = 10g + g - 7 - 9$
Combine Like Terms: Combine like terms: $\newline$ $10g + g = 11g$ $\newline$ $-7 - 9 = -16$ $\newline$ So, $(10g - 7) + (g - 9)$ simplifies to $11g - 16$
Multiply by $2$ : Now, multiply this expression by $2$ to find the perimeter: $\newline$ $P = 2 \times (11g - 16)$
Distribute the $2$ : Distribute the $2$ into the expression: $\newline$ $P = 2 \times 11g - 2 \times 16$
Perform Multiplication: Perform the multiplication: $P = 22g - 32$

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