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.
Similar Questions
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Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
