The area of square field is half hectare. Find the length of its diagonal in meter
To find the length of the diagonal of a square field, we need to know the length of one side of the square.
In this case, we are given that the area of the square field is half a hectare.
To find the length of one side of the square, we can use the formula for the area of a square: Area = side^2.
In this case, the area is half a hectare, which is equal to 5000 square meters (as 1 hectare is equal to 10,000 square meters).
So we can write the equation: 5000 = side^2.
To find the length of one side of the square, we need to take the square root of both sides of the equation. √5000 = √side^2.
The square root of 5000 is approximately 70.71 meters.
Now that we know the length of one side of the square, we can find the length of the diagonal using Pythagoras' theorem.
In a square, the diagonal forms a right triangle with two sides being the length of one side of the square. The diagonal is the hypotenuse of this right triangle.
Using Pythagoras' theorem, we can write the equation: diagonal^2 = side^2 + side^2.
Substituting the length of one side of the square (70.71 meters) into the equation, we get: diagonal^2 = 70.71^2 + 70.71^2.
Calculating this equation, we find that diagonal^2 = 10000 meters^2.
Therefore, the length of the diagonal is the square root of 10000, which is 100 meters.
So, the length of the diagonal of the square field is 100 meters.
To find the length of the diagonal of a square field, we can use the formula:
diagonal length = side length * √2
Given that the area of the square field is half a hectare, we need to convert it to square meters because the unit for the diagonal length is meters.
1 hectare = 10,000 square meters
Therefore, half a hectare is equal to:
1/2 * 10,000 = 5,000 square meters
Since the area of a square is calculated by squaring the side length, we can find the side length of the square field by taking the square root of the area:
side length = √(area)
side length = √(5,000)
Now we can calculate the diagonal length using the formula mentioned earlier:
diagonal length = side length * √2
diagonal length = √(5,000) * √2
diagonal length ≈ 70.71 meters
Therefore, the length of the diagonal of the square field is approximately 70.71 meters.
one hectare is 10,000 m^2 , (100 m by 100m)
so half of that is 5,000 m^2
so let each side be x
then x^2 = 5000
for the diagonal d,
d^2 = x^2 + x^2 = 2x^2 = 10000
d = 100 m