Question

alissa is framing a rectangular picture with length 10 inches and width 8 inches. let x represent the width of the frame in inches.
which expression represents the length, in inches, of the framed picture?
2x + 10
complete
which expression represents the width of the framed picture?
2x + 8
complete
what is the perimeter of the framed picture in terms of x?
( \boxed{\quad} x + \boxed{\quad} ) inches
done

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \).

Step2: Identify Framed Length and Width

From the problem, the length of the framed picture is \( 2x + 10 \) and the width is \( 2x + 8 \).

Step3: Substitute into Perimeter Formula

Substitute length and width into the formula:
\[

$$\begin{align*} P &= 2\times((2x + 10) + (2x + 8))\\ &= 2\times(2x + 10 + 2x + 8)\\ &= 2\times(4x + 18)\\ &= 8x + 36 \end{align*}$$

\]
We can rewrite \( 8x + 36 \) in the form \( (\square x + \square) \) as \( 8x + 36 \), so the coefficient of \( x \) is 8 and the constant term is 36.

Answer:

8, 36