Perimeter of a Rectangle:
The perimeter of a rectangle is the sum of all its sides. In a rectangle, opposite sides are equal in length. Therefore, if we let the length of the rectangle be L and the breadth be B, then the perimeter (P) can be calculated using the formula:

P = 2L + 2B

Given Information:
According to the given information, the length of the rectangle is 5/4 times its breadth. Let's represent the breadth as B.

Length (L) = (5/4)B

The perimeter of the rectangle is given as 81 meters. So, we can write the equation:

2L + 2B = 81

Now, we can substitute the value of L from the given relationship into the equation:

2(5/4)B + 2B = 81

Solving for B:
To solve the equation, we need to simplify and solve for the variable B.

Multiplying 2 by (5/4) gives us (10/4)B:

(10/4)B + 2B = 81

Combining like terms:

(10/4 + 8/4)B = 81

(18/4)B = 81

Simplifying the fraction:

(9/2)B = 81

To isolate B, we can multiply both sides of the equation by the reciprocal of (9/2), which is (2/9):

B = (81 * 2/9)

Simplifying:

B = 18

Calculating the Length:
Now that we have found the value of B, we can substitute it back into the relationship between L and B:

L = (5/4) * 18

Simplifying:

L = 22.5

Calculating the Area:
The area of a rectangle is given by the formula:

A = L * B

Substituting the values we obtained:

A = 22.5 * 18

Calculating the product:

A = 405 square meters

Conclusion:
The area of the rectangle is 405 square meters. By solving the equation using the given information, we found that the breadth of the rectangle is 18 meters and the length is 22.5 meters.

1645 m2