The area of a square is 24 sq cm less than one seventh the area of a rectangle. The length of the rectangle is 35 cm and its breadth is 14 cm less than its length. What is the perimeter of the square ?

Options

A. 72 cm
B. 44 cm
C. 36 cm
D. cannot be determined

Answer

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

### Step 1: Find the dimensions of the rectangle
We know the length of the rectangle is given as 35 cm. The breadth (width) of the rectangle is 14 cm less than its length.

**Calculation:**
- Length of the rectangle (L) = 35 cm
- Breadth of the rectangle (B) = Length - 14 cm = 35 cm - 14 cm = 21 cm

### Step 2: Calculate the area of the rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

**Calculation:**
- Area of the rectangle = 35 cm × 21 cm = 735 cm²

### Step 3: Calculate one-seventh of the area of the rectangle
Now, we need to find one-seventh of the area of the rectangle.

**Calculation:**
- One-seventh of the area = \( \frac{735}{7} \) = 105 cm²

### Step 4: Find the area of the square
According to the problem, the area of the square is 24 cm² less than one-seventh of the area of the rectangle.

**Calculation:**
- Area of the square = One-seventh of the area of the rectangle - 24 cm²
- Area of the square = 105 cm² - 24 cm² = 81 cm²

### Step 5: Calculate the side length of the square
To find the side length of the square, we take the square root of the area.

**Calculation:**
- Side of the square = \( \sqrt{81} \) = 9 cm

### Step 6: Calculate the perimeter of the square
The perimeter of a square is calculated using the formula:
\[ \text{Perimeter} = 4 \times \text{Side} \]

**Calculation:**
- Perimeter of the square = 4 × 9 cm = 36 cm

### Final Answer:
The perimeter of the square is **36 cm**.

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