Sure, let's tackle this problem step-by-step.
### Step 1: Define Variables
1. Dimensions of the screen:
- Length of the screen = 8 inches
- Width of the screen = 5 inches
2. Thickness of the border:
- Let [tex]\( t \)[/tex] represent the thickness of the border in inches
### Step 2: Determine the Total Length and Total Width
Since the border surrounds the entire screen, it adds thickness to both sides of the screen. Therefore:
1. Total Length of the Tablet:
- The border adds [tex]\( t \)[/tex] inches to both the top and the bottom.
- Hence, the total length of the tablet = [tex]\( 8 + 2t \)[/tex]
2. Total Width of the Tablet:
- The border adds [tex]\( t \)[/tex] inches to both the left and the right.
- Hence, the total width of the tablet = [tex]\( 5 + 2t \)[/tex]
### Step 3: Write an Expression for the Total Area
The total area of the tablet, including the frame, can be found by multiplying the total length by the total width:
Total area [tex]\( = (\text{Total Length}) \times (\text{Total Width}) \)[/tex]
Substitute the expressions we found for the total length and width:
[tex]\[ \text{Total Area} = (8 + 2t) \times (5 + 2t) \][/tex]
### Summary
Your final expressions are:
- Total length of the tablet: [tex]\( 8 + 2t \)[/tex]
- Total width of the tablet: [tex]\( 5 + 2t \)[/tex]
- Total area of the tablet: [tex]\( (8 + 2t) \times (5 + 2t) \)[/tex]
So, the expression for the total area of the tablet, including the frame, is:
[tex]\[ (8 + 2t) \times (5 + 2t) \][/tex]
