Rectangular Plot Dimensions and Perimeter
Let the breadth of the rectangular plot be B meters and the length be L meters.
According to the problem statement:
- The length is twice the breadth: \( L = 2B \)
- The diagonal (D) is \( 6\sqrt{5} \) m.
Calculating Plot Dimensions
For a rectangle, the relationship between length, breadth, and diagonal is given by the Pythagorean theorem: \( D^2 = L^2 + B^2 \).
Substitute the given values and the relationship \( L = 2B \) into the formula:
\( (6\sqrt{5})^2 = (2B)^2 + B^2 \)
\( 36 \times 5 = 4B^2 + B^2 \)
\( 180 = 5B^2 \)
Now, solve for \( B^2 \):
\( B^2 = \frac{180}{5} \)
\( B^2 = 36 \)
Taking the square root to find the breadth (since length must be positive):
\( B = \sqrt{36} = 6 \) m
Now, find the length using \( L = 2B \):
\( L = 2 \times 6 = 12 \) m
Finding the Perimeter
The perimeter (P) of a rectangle is calculated using the formula \( P = 2(L + B) \).
Substitute the values of L and B:
\( P = 2(12 + 6) \)
\( P = 2(18) \)
\( P = 36 \) m
Therefore, the perimeter of the plot is 36 m.
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