Question

The difference between length and breadth of a rectangle is 15m. If the perimeter of rectangle is 162 m, then the area of the rectangle (in m²) is

• A. 3168
• B. 2524
• C. 1872
• D. 1584

Answer 1

The Correct Option is D

To solve for the area of the rectangle, let's denote the length by \( l \) and the breadth by \( b \). We are given two key pieces of information:

1. The difference between the length and the breadth is 15m. This can be expressed as:
   \( l - b = 15 \)
   (Equation 1)
2. The perimeter of the rectangle is 162m. The formula for the perimeter of a rectangle is \( 2(l+b) \). Therefore:
   \( 2(l+b) = 162 \)
   Dividing both sides by 2, we get:
   \( l + b = 81 \)
   (Equation 2)

We now solve these two equations simultaneously:

1. From Equation 1: \( l = b + 15 \)
2. Substitute \( l = b + 15 \) into Equation 2:
   \( (b + 15) + b = 81 \)
3. Simplify:
   \( 2b + 15 = 81 \)
4. Subtract 15 from both sides:
   \( 2b = 66 \)
5. Divide by 2 to solve for \( b \):
   \( b = 33 \)
6. Substitute \( b = 33 \) back into \( l = b + 15 \):
   \( l = 33 + 15 = 48 \)

With these values, calculate the area of the rectangle using the formula \( \text{Area} = l \times b \):
\(\text{Area} = 48 \times 33 = 1584 \, \text{m}^2\)

Therefore, the area of the rectangle is 1584 m².