A 2 cm wide wooden strip is to be fixed on a photo of 40 cm x 30 cm size all along its four sides. What is the minimum length of the wooden strip required?
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.
Important Questions from Mensuration 2D (Notes)
- $P_1$ and $P_2$ are two regular polygons. The sum of all the interior angles of $P_1$ is $1800^\circ$. Each interior angle of $P_2$ exceeds its exterior angle by $120^\circ$. The difference between the number of sides of $P_1$ and $P_2$ is:
- The perimeter of the triangle is 24 cm and if the sides of the triangles are by prime numbers then the half of the area of triangle (in $cm^2$) is:
- The area of a square is 324 cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
- If the area of a rhombus is $10 \text{ cm}^2$ and one of its interior angles is $150^\circ$, what is the perimeter (in cm) of the rhombus?
- If the area of a rhombus is 10 cm$^2$ and one of its interior angles is 150°, what is the perimeter (in cm) of the rhombus?
