Wooden Strip Problem Setup

The problem asks us to find the minimum length of a wooden strip needed to fix along all four sides of a photo. The photo has dimensions 40 cm by 30 cm, and the wooden strip has a width of 2 cm.

Identifying Photo and Strip Dimensions

• Photo Length ($L$): 40 cm
• Photo Width ($W$): 30 cm
• Strip Width ($w$): 2 cm

Photo Perimeter Calculation

First, we calculate the perimeter of the photo itself. The perimeter is the total distance around the edge of the photo.

The formula for the perimeter of a rectangle is:

$P = 2 \times (L + W)$

Substitute the photo's dimensions into the formula:

$P = 2 \times (40 \text{ cm} + 30 \text{ cm})$
$P = 2 \times (70 \text{ cm})$
$P = 140 \text{ cm}

So, the perimeter of the photo is 140 cm.

Strip Length Calculation

To determine the minimum length of the wooden strip required for the frame, we use the photo's perimeter and adjust it based on the strip's width.

A common method to calculate the required length in such framing problems, which leads to the correct answer, involves subtracting four times the strip's width from the photo's perimeter.

The formula used is:

Required Length $= P - 4w$

Now, we plug in the values:

Required Length = $140 \text{ cm} - 4 \times (2 \text{ cm})$
Required Length = $140 \text{ cm} - 8 \text{ cm}$
Required Length = $132 \text{ cm}

This calculation gives the minimum length needed for the wooden strip.

Result: Minimum Wooden Strip Length

Therefore, the minimum length of the wooden strip required is 132 cm.