Question

the rectangle in the diagram provided has a perimeter of 9y + 68 centimeters. diagram of rectangle with length 4y + 8 and width 3y + 6 which of the following equations represents the perimeter in terms of y? 9y + 68 = 12y + 18; 9y + 68 = 14y + 28; 9y + 68 = 7y + 18; 9y + 68 = 7y + 14

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, length is \( 4y + 8 \) and width is \( 3y + 6 \).

Step2: Calculate perimeter using formula

Substitute length and width into the formula:
\( P = 2\times((4y + 8) + (3y + 6)) \)
Simplify inside the parentheses: \( (4y + 8)+(3y + 6)=7y + 14 \)
Then multiply by 2: \( P = 2\times(7y + 14)=14y + 28 \)
The given perimeter is \( 9y + 68 \), so the equation is \( 9y + 68 = 14y + 28 \).

Answer:

\( 9y + 68 = 14y + 28 \) (the option with this equation)