Question

The length and breadth of a rectangular shaped room are 15 units and 12 units respectively. If the room is extended by increasing both the length and breadth by 1 unit, then the floor area of the extended room is

• A. 218 sq.units
• B. 206 sq.units
• C. 208 sq.units
• D. 218 sq.units

Hint:

Be sure to apply the 1-unit increase directly to the dimensions *before* multiplying. Do not add 1 directly to the old area. \[ \text{New Area} = 16 \times 13 = 208 \text{ sq. units} \]

Answer 1

The Correct Option is C

Concept: The surface floor area (\(A\)) enclosed inside a two-dimensional geometric rectangle is calculated by multiplying its linear length (\(l\)) by its linear breadth (\(b\)): \[ \text{Area } (A) = \text{Length } (l) \times \text{Breadth } (b) \] When changes are made to these dimensions, we first calculate the new dimensions before computing the modified area.

Step 1: Identify the initial dimensions of the room.
From the problem statement, the starting values are:
• Initial length (\(l_{\text{old}}\)) = 15 units
• Initial breadth (\(b_{\text{old}}\)) = 12 units

Step 2: Calculate the new dimensions after the expansion.
The problem states that both the length and the breadth are increased by exactly 1 unit: \[ \text{New Length } (l_{\text{new}}) = l_{\text{old}} + 1 = 15 + 1 = 16 \text{ units} \] \[ \text{New Breadth } (b_{\text{new}}) = b_{\text{old}} + 1 = 12 + 1 = 13 \text{ units} \]

Step 3: Compute the floor area of the expanded room.
Multiply the newly calculated dimensions together: \[ \text{Extended Floor Area} = l_{\text{new}} \times b_{\text{new}} \] \[ \text{Extended Floor Area} = 16 \times 13 \] Let us break down this multiplication: \[ 16 \times 13 = 16 \times (10 + 3) \] \[ 16 \times 13 = (16 \times 10) + (16 \times 3) \] \[ 16 \times 13 = 160 + 48 = 208 \text{ sq. units} \] The floor area of the extended room is exactly 208 square units. This matches Option (C).