Find the approximate value which should replace the question mark (?) in each of the following question .
The ratio between the length and breadth of rectangular plot is 7:5 , If the perimeter of the plot is 144 metres,What is its area?

Options

A. 1320 sq.metres
B. 1260 sq.metres
C. 1280 sq.metres
D. 1380 sq.metres

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the ratio
The ratio of the length (L) to the breadth (B) of the rectangular plot is given as 7:5. This means we can express the length and breadth in terms of a variable \( x \):
- Length \( L = 7x \)
- Breadth \( B = 5x \)

**Hint:** Remember that the ratio can be expressed as multiples of a common variable.

### Step 2: Use the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(L + B) \]
Substituting the expressions for length and breadth, we have:
\[ P = 2(7x + 5x) = 2(12x) = 24x \]

**Hint:** The perimeter is the total distance around the rectangle, which involves both length and breadth.

### Step 3: Set up the equation with the given perimeter
We know from the problem that the perimeter is 144 meters. Therefore, we can set up the equation:
\[ 24x = 144 \]

**Hint:** Setting the equation allows us to find the value of \( x \).

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 24:
\[ x = \frac{144}{24} = 6 \]

**Hint:** Division helps isolate the variable to find its value.

### Step 5: Calculate the length and breadth
Now that we have \( x \), we can find the actual length and breadth:
- Length \( L = 7x = 7 \times 6 = 42 \) meters
- Breadth \( B = 5x = 5 \times 6 = 30 \) meters

**Hint:** Substitute the value of \( x \) back into the expressions for length and breadth.

### Step 6: Calculate the area
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 42 \times 30 = 1260 \, \text{square meters} \]

**Hint:** The area is calculated by multiplying the length and breadth together.

### Final Answer
The area of the rectangular plot is **1260 square meters**.

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