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?
x + 10
2x + 10
x² + 10
10x²

Explanation:

Step1: Analyze the frame's length contribution

The original picture length is 10 inches. The frame has a width \( x \) on the top and bottom (or in the length direction, left and right? Wait, no, for length: the frame adds \( x \) on the left and \( x \) on the right? Wait, no, the length of the picture is vertical? Wait, the diagram: the green rectangle has length 10 (vertical) and width 8 (horizontal). So the framed picture's length (vertical) would have \( x \) at the top and \( x \) at the bottom. Wait, no, maybe I got length and width mixed. Wait, the problem says "length of the framed picture". The original picture: length 10 (let's say vertical), width 8 (horizontal). The frame has width \( x \): so on the vertical sides (length direction), the frame adds \( x \) on the top and \( x \) on the bottom? Wait, no, looking at the diagram: the horizontal direction (width of picture is 8) has \( x \) on left and right. The vertical direction (length of picture is 10) has \( x \) on top and bottom. So the length of the framed picture (vertical) would be original length (10) plus \( x \) (top) plus \( x \) (bottom) = \( 10 + x + x = 2x + 10 \).

Step2: Match with options

The options are \( x + 10 \), \( 2x + 10 \), \( x^2 + 10 \), \( 10x^2 \). From step1, the expression is \( 2x + 10 \).

Answer:

\( 2x + 10 \) (corresponding to the option "2x + 10")