Question

6 the rectangle in the diagram provided has a perimeter of 7y + 91 centimeters. diagram with length 5y+8 and width 3y+6 6a which of the following equations represents the perimeter in terms of y? 7y + 91 = 7y + 14; 7y + 91 = 7y + 18; 7y + 91 = 14y + 28; 7y + 91 = 10y + 46

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 \( 5y + 8 \) and width is \( 2y + 6 \).

Step2: Substitute length and width into formula

\[

$$\begin{align*} P&=2\times((5y + 8)+(2y + 6))\\ &=2\times(5y + 8 + 2y + 6)\\ &=2\times(7y + 14)\\ &=14y + 28 \end{align*}$$

\]
We know the perimeter is also given as \( 7y + 91 \), so the equation is \( 7y + 91 = 14y + 28 \).

Answer:

\( 7y + 91 = 14y + 28 \) (the option with this equation)