Question

The perimeter of a rectangle is 72 cm. If its length is 22 cm, then its breadth is:

• A. 12 cm
• B. 14 cm
• C. 16 cm
• D. 18 cm

Hint:

To solve perimeter problems mentally, use the semi-perimeter concept! The semi-perimeter ($\text{length} + \text{breadth}$) is always exactly half of the total perimeter. $$\text{Half of } 72 = 36 \text{ cm}$$ $$\text{Breadth} = 36 - \text{Length} = 36 - 22 = 14 \text{ cm!}$$

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The perimeter of a two-dimensional geometric rectangle represents the total boundary length enclosing its surface. Because a rectangle features two parallel lengths that are equal and two parallel breadths that are equal, its perimeter is equal to twice the sum of its length and breadth.

Step 2: Key Formula or Approach:
The standard geometric formula for the perimeter ($P$) of a rectangle is: $$P = 2 \times (l + b)$$ Where: $l = \text{length of the rectangle}$ $b = \text{breadth of the rectangle}$

Step 3: Detailed Explanation:
Substitute the given values from the problem description into our formula: $\text{Perimeter } (P) = 72 \text{ cm}$ $\text{Length } (l) = 22 \text{ cm}$ \[ 72 = 2 \times (22 + b) \] Divide both sides of the equation by 2 to isolate the linear sum: \[ \frac{72}{2} = 22 + b \] \[ 36 = 22 + b \] Now, isolate the breadth variable ($b$) by subtracting 22 from 36: \[ b = 36 - 22 \] \[ b = 14 \text{ cm} \]

Step 4: Final Answer:
The breadth of the rectangle is 14 cm.