Question

the perimeter formula for a rectangle is ( 2l + 2w ), where ( l ) is the length and ( w ) is the width. complete the steps to find an expression that represents the perimeter of the rectangle.

1. substitute the expressions for length and width into the formula ( 2l + 2w ).
2. distribute 2 to each term in the parentheses.
3. combine like terms. inches

Explanation:

Step1: Substitute length and width

Substitute \( l = 8x - 1 \) and \( w=2x + 4 \) into \( 2l+2w \).
\( 2(8x - 1)+2(2x + 4) \)

Step2: Distribute

Use the distributive property \( a(b + c)=ab+ac \).
\( 2\times8x-2\times1+2\times2x + 2\times4=16x-2 + 4x+8 \)

Step3: Combine like terms

Combine the \( x \) - terms (\( 16x+4x \)) and the constant terms (\( - 2 + 8 \)).
\( (16x+4x)+(-2 + 8)=20x+6 \)

Answer:

\( 20x + 6 \)