A poster has a rectangular printed area 100 cm by 140 cm and a blank strip of uniform width around the edges. The perimeter of the poster is 
1 3/4
 times the perimeter of the printed area. What is the width of the blank strip?

We are tasked with determining the width of the blank strip around a rectangular printed area of a poster, where the perimeter of the entire poster is \( \frac{7}{4} \) (or 1.75) times the perimeter of the printed area.

### Step 1: Define the dimensions of the printed area and the total poster.
- The printed area is 100 cm by 140 cm.
- Let the width of the blank strip around the edges be denoted by \( x \) cm.

### Step 2: Calculate the perimeter of the printed area.
The perimeter \( P_{\text{printed}} \) of a rectangle is given by:

\[
P_{\text{printed}} = 2 \times (\text{length} + \text{width}) = 2 \times (140 + 100) = 2 \times 240 = 480 \text{ cm}.
\]

### Step 3: Set up the equation for the perimeter of the entire poster.
The total poster will have dimensions increased by the width of the strip \( x \) on all sides, so the new dimensions are:
- Length: \( 140 + 2x \),
- Width: \( 100 + 2x \).

The perimeter \( P_{\text{total}} \) of the poster is then:

\[
P_{\text{total}} = 2 \times ((140 + 2x) + (100 + 2x)) = 2 \times (240 + 4x) = 480 + 8x.
\]

### Step 4: Use the condition on the perimeters.
We are given that the perimeter of the entire poster is \( \frac{7}{4} \) times the perimeter of the printed area. Thus, we have:

\[
P_{\text{total}} = \frac{7}{4} \times P_{\text{printed}}.
\]

Substitute the known values:

\[
480 + 8x = \frac{7}{4} \times 480 = 840.
\]

### Step 5: Solve for \( x \).
Now, solve the equation \( 480 + 8x = 840 \):

\[
8x = 840 - 480 = 360,
\]

\[
x = \frac{360}{8} = 45.
\]

### Final Answer:
The width of the blank strip is \( \boxed{45} \) cm.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What is the area of the printed portion of the poster?
2. What would the area of the entire poster be after adding the blank strip?
3. How would the result change if the perimeter of the poster was doubled instead of being \( \frac{7}{4} \) times the printed area’s perimeter?
4. How do you calculate the total area added by the blank strip around the edges?
5. What would the width of the blank strip be if the printed area had different dimensions?

**Tip**: When solving word problems, clearly define all variables and relationships before jumping into calculations to avoid confusion.

A poster has a rectangular printed area 100 cm by 140 cm and a blank strip of uniform width around the edges. The perimeter of the poster is 1 3/4 times the perimeter of the printed area. What is the width of the blank strip?

Solve a problem where a rectangular poster with a printed area of 100 cm by 140 cm has a uniform blank strip around its edges. The perimeter of the poster is 1.75 times the perimeter of the printed area. Learn how to determine the width of the blank strip using algebra and geometry. Suitable for Grades 8-10.

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