The length of a rectangle is 6 metres more than the side of a square and the ‘breadth of the rectangle is 6 metres less than the side of the same square. If the area of the square is 625 square metres, what is the area of the rectangle? (in sq meter)

Options

A. 665
B. 551
C. 627
D. 589

Answer

To solve the problem step by step, we will first determine the side of the square, then use that to find the dimensions of the rectangle, and finally calculate the area of the rectangle.

### Step 1: Find the side of the square.
The area of the square is given as 625 square meters. The area of a square is calculated using the formula:
\[ \text{Area} = \text{side}^2 \]

Let the side of the square be \( s \). Therefore, we can write:
\[ s^2 = 625 \]

To find \( s \), we take the square root of both sides:
\[ s = \sqrt{625} \]
\[ s = 25 \text{ meters} \]

### Step 2: Determine the length of the rectangle.
According to the problem, the length of the rectangle is 6 meters more than the side of the square:
\[ \text{Length of rectangle} = s + 6 \]
Substituting the value of \( s \):
\[ \text{Length of rectangle} = 25 + 6 = 31 \text{ meters} \]

### Step 3: Determine the breadth of the rectangle.
The breadth of the rectangle is 6 meters less than the side of the square:
\[ \text{Breadth of rectangle} = s - 6 \]
Substituting the value of \( s \):
\[ \text{Breadth of rectangle} = 25 - 6 = 19 \text{ meters} \]

### Step 4: Calculate the area of the rectangle.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Substituting the values we found:
\[ \text{Area of rectangle} = 31 \times 19 \]

Now, we calculate:
\[ 31 \times 19 = 589 \text{ square meters} \]

### Final Answer:
The area of the rectangle is **589 square meters**.

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