A square carpet with an area 169 `m^(2)` must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangualar room. What is the area of rectangular room?

Options

A. `180 m^(2)`
B. `164 m^(2)`
C. `152 m^(2)`
D. `143 m^(2)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the side length of the square carpet.
The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
Given that the area of the square carpet is \(169 \, m^2\), we can find the side length by taking the square root of the area:
\[ \text{side} = \sqrt{169} = 13 \, m \]

### Step 2: Determine the new dimensions after cutting.
We need to cut 2 meters off one edge of the carpet. The original side length of the carpet is 13 meters. After cutting 2 meters, the new length of that side will be:
\[ \text{New side length} = 13 \, m - 2 \, m = 11 \, m \]
The other side remains unchanged at 13 meters.

### Step 3: Calculate the area of the rectangular room.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{length} \times \text{breadth} \]
In this case, the length is 13 meters and the breadth is 11 meters. Therefore, the area of the rectangular room is:
\[ \text{Area} = 13 \, m \times 11 \, m = 143 \, m^2 \]

### Conclusion:
The area of the rectangular room is \(143 \, m^2\).

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