Question

. give the perimeter of the rectangle below in simplest form
\boxed{\

$$\begin{array}{|c|}\\hline\\quad\\quad\\quad\\quad\\quad\\quad\\\\\\hline\\end{array}$$

}\quad y + 9
4y - 1

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( 4y - 1 \) and the width is \( y + 9 \).

Step2: Substitute the length and width into the formula

Substitute the values into the formula: \( P = 2\times[(4y - 1)+(y + 9)] \).

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (4y - 1)+(y + 9)=4y + y - 1 + 9 = 5y + 8 \).

Step4: Multiply by 2 to get the perimeter

Now, multiply the simplified expression by 2: \( P = 2\times(5y + 8)=10y + 16 \).

Answer:

\( 10y + 16 \)