The perimeter of a rectangular grassy plot is 189 m and its breadth is 10.5 m . Find the length and area of the plot .

Answer

To solve the problem step by step, we will use the given information about the perimeter and breadth of the rectangular plot.

### Step 1: Understand the formula for the perimeter of a rectangle.
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter is 189 m and the breadth is 10.5 m. Substituting these values into the formula gives:
\[ 189 = 2(L + 10.5) \]

### Step 3: Simplify the equation to find \( L + B \).
Divide both sides of the equation by 2:
\[ L + 10.5 = \frac{189}{2} \]
Calculating the right side:
\[ L + 10.5 = 94.5 \]

### Step 4: Solve for the length \( L \).
Now, subtract the breadth from both sides:
\[ L = 94.5 - 10.5 \]
Calculating this gives:
\[ L = 84 \text{ m} \]

### Step 5: Calculate the area of the rectangular plot.
The area (A) of a rectangle is given by:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 84 \times 10.5 \]

### Step 6: Perform the multiplication to find the area.
Calculating this gives:
\[ A = 882 \text{ m}^2 \]

### Final Answer:
- Length of the rectangular plot: **84 m**
- Area of the rectangular plot: **882 m²**

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