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: Find the original side length.
Area of a square = side^2, so original side = sqrt(3600) = 60 ft.
Step 2: Double the side.
New side = 2 x 60 = 120 ft.
Step 3: Calculate the new area.
Doubling the side quadruples the area (new area = 4 x original). \[ 120^2 = 4 \times 3600 = 14400 \text{ sq.ft} \] \[ \boxed{14400 \text{ sq.ft}} \]