Question

The area of a square shaped plot is 3600 sq.ft. If the lengths of all the sides of the plot are doubled, then the area of the plot is

• A. 14600 sq.ft
• B. 14800 sq.ft
• C. 12200 sq.ft
• D. 14400 sq.ft

Hint:

Always remember the scaling rule of geometry:
- Length scales by $k$
- Area scales by $k^2$
- Volume scales by $k^3$
Since the side was doubled (scaled by 2), the area must scale by $2^2 = 4$. Simply multiply $3600 \times 4 = 14400$.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given that the area of a square plot is 3600 square feet.
We need to find the new area of this plot if all its side lengths are doubled.

Step 2: Key Formula or Approach:
1.

Formula for area of a square:
\[ \text{Area} = s^2 \]
where $s$ is the side length.
2.

Scaling Rule for Area:
If the linear dimensions (like sides) of a two-dimensional shape are scaled by a factor of $k$, then its area is scaled by a factor of $k^2$:
\[ \text{New Area} = \text{Old Area} \times k^2 \]

Step 3: Detailed Calculation:

Method 1: Direct Scaling (Easiest)
- Here, the sides are doubled, so the scale factor $k = 2$.
- The scaling factor for the area will be:
\[ k^2 = 2^2 = 4 \]
- Calculate the new area:
\[ \text{New Area} = 3600 \times 4 = 14400 \text{ sq.ft} \]

Method 2: Step-by-Step Dimension Calculation
- Initial Area = 3600 sq.ft
- Side length ($s$):
\[ s = \sqrt{3600} = 60 \text{ ft} \]
- If sides are doubled, the new side length ($S$) becomes:
\[ S = 2 \times 60 = 120 \text{ ft} \]
- Calculate the new area:
\[ \text{New Area} = S^2 = 120^2 = 14400 \text{ sq.ft} \]
Both methods yield the same result.

Step 4: Final Answer:
The new area is 14400 sq.ft, corresponding to Option (D).