The length and breadth of a painting is 15 cm and 10 cm respectively. A 1 cm wide boarder is made around the painitng.
What is the area of boarder?

Options

A. 60 sq cm.
B. 45 sq cm.
C. 54 sq cm.
D. 16 sq cm.

Answer

To find the area of the border around the painting, we can follow these steps:

### Step 1: Identify the dimensions of the painting
The length (L) of the painting is given as 15 cm and the breadth (B) is given as 10 cm.

### Step 2: Determine the dimensions of the outer rectangle (including the border)
Since there is a 1 cm wide border around the painting, we need to add 2 cm to both the length and the breadth (1 cm on each side).

- Outer Length = L + 2 * Width of Border = 15 cm + 2 * 1 cm = 15 cm + 2 cm = 17 cm
- Outer Breadth = B + 2 * Width of Border = 10 cm + 2 * 1 cm = 10 cm + 2 cm = 12 cm

### Step 3: Calculate the area of the outer rectangle
The area of the outer rectangle (including the border) can be calculated using the formula:
\[ \text{Area}_{\text{outer}} = \text{Outer Length} \times \text{Outer Breadth} \]
\[ \text{Area}_{\text{outer}} = 17 \, \text{cm} \times 12 \, \text{cm} = 204 \, \text{cm}^2 \]

### Step 4: Calculate the area of the painting
The area of the painting can be calculated using the formula:
\[ \text{Area}_{\text{painting}} = \text{Length} \times \text{Breadth} \]
\[ \text{Area}_{\text{painting}} = 15 \, \text{cm} \times 10 \, \text{cm} = 150 \, \text{cm}^2 \]

### Step 5: Calculate the area of the border
The area of the border is the difference between the area of the outer rectangle and the area of the painting:
\[ \text{Area}_{\text{border}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{painting}} \]
\[ \text{Area}_{\text{border}} = 204 \, \text{cm}^2 - 150 \, \text{cm}^2 = 54 \, \text{cm}^2 \]

### Final Answer
The area of the border is **54 cm²**.

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