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The width of a rectangle measures
(6f+g) centimeters, and its length measures
(2f+7g) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

16 f+16

8+8f

16 g+16 f

1+14 g+16 f

The width of a rectangle measures $(6 f+g)$ centimeters, and its length measures $(2 f+7 g)$ centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? $\newline$ $16 f+16$ $\newline$ $8+8 f$ $\newline$ $16 g+16 f$ $\newline$ $1+14 g+16 f$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The width of a rectangle measures

(6 f+g)

centimeters, and its length measures

(2 f+7 g)

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

\newline

16 f+16

\newline

8+8 f

\newline

16 g+16 f

\newline

1+14 g+16 f

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 $P = 2 \times (\text{length} + \text{width})$ .
Substitute Given Values: The given width of the rectangle is $(6f+g)$ cm and the length is $(2f+7g)$ cm. We substitute these expressions into the perimeter formula: $P = 2 \times ((6f+g) + (2f+7g))$ .
Simplify Expression: Now we simplify the expression inside the parentheses: $6f+g$ + $2f+7g$ = $6f + 2f + g + 7g$ = $8f + 8g$ .
Multiply by $2$ : Next, we multiply the simplified expression by $2$ to find the perimeter: $P = 2 \times (8f + 8g) = 2 \times 8f + 2 \times 8g = 16f + 16g$ .
Check Answer Choices: We check the answer choices to see which one matches our expression for the perimeter. The correct expression that represents the perimeter is $16f + 16g$ .

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