the length of a rectangle is 5/4th of breadth. if its perimeter is 81 m, find area.
2(b + 5/4 b) = 81
...
Now that you have b, the area is
b * 5/4 b = 5/4 b^2
Solution
To find the area of a rectangle, we need to know the length and breadth (or width) of the rectangle. In this case, you are given that the length of the rectangle is 5/4th of the breadth. Let's assume the breadth of the rectangle is "x" meters.
According to the information given, the length of the rectangle is (5/4) * x meters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 81 meters.
The formula for the perimeter of a rectangle is: Perimeter = 2 * (Length + Breadth).
So, from the given information, we can write the equation as: 2 * [(5/4) * x + x] = 81.
Let's solve this equation to find the value of x:
2 * [(5/4) * x + x] = 81
2 * [(9/4) * x] = 81
[(9/4) * x] = 81/2
9x/4 = 81/2
9x = (81/2) * 4
9x = 81 * 2
9x = 162
x = 162/9
x = 18
So, the breadth of the rectangle is 18 meters.
Now, we can calculate the length of the rectangle using the value of x:
Length = (5/4) * x
Length = (5/4) * 18
Length = 90/4
Length = 22.5 meters
The area of a rectangle is calculated by multiplying its length and breadth. So, the area is:
Area = Length * Breadth
Area = 22.5 * 18
Area = 405 square meters.
Hence, the area of the rectangle is 405 square meters.