the length of the rectangular field is thrice of its width if the perimeter of this field is 1.6 kilometres find its area in metre square
width --- x
length ---- 3x
2(x+3x) = 1.6 km
8x = 1600 m
x = 200
then 3x = 600
The field is 200 m by 600 m for an area of
120,000 m^2
To find the area of the rectangular field, we need to first determine its dimensions (length and width) using the given information.
Let's assume the width of the rectangular field is "x" meters. As per the problem, the length is three times the width, so the length would be 3x meters.
To find the perimeter, we sum the lengths of all four sides of the rectangle.
Perimeter of a rectangle = 2(length + width)
Given that the perimeter is 1.6 kilometers (1 kilometer = 1000 meters), we can convert it to meters:
Perimeter = 1.6 km = 1.6 * 1000 m = 1600 m
Using the formula for the perimeter, we have:
1600 = 2(3x + x)
Simplifying the equation:
1600 = 2(4x)
800 = 4x
x = 800 / 4
x = 200 meters
Now that we have the width (x = 200 meters), we can find the length by multiplying it by 3:
Length = 3 * 200 = 600 meters
To find the area of the rectangular field, we use the formula:
Area of a rectangle = Length * Width
Area = 200 * 600 = 120,000 square meters
Therefore, the area of the rectangular field is 120,000 square meters.