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.