The area of a square field is 3/2 hectares find the length of its diagonal in metres please help.
To find the length of the diagonal of a square field, we need to find the length of one side of the square first.
Given that the area of the square field is 3/2 hectares, we can convert it to square meters as follows:
1 hectare = 10,000 square meters
Therefore, 3/2 hectare = (3/2) * (10,000) square meters = 15,000 square meters.
Since a square has equal sides, the area of a square is given by the formula:
Area of the square = side * side
Therefore, we have:
15,000 square meters = side * side
To find the side length, we can take the square root of both sides of the equation:
√(15,000 square meters) = √(side * side)
Simplifying:
√(15,000) = side
Now let's calculate the square root of 15,000:
√15,000 ≈ 122.47 meters
Therefore, the length of one side of the square field is approximately 122.47 meters.
To find the length of the diagonal, we can use the Pythagorean theorem:
In a square, the diagonal is the hypotenuse of a right triangle formed by the two sides (legs) of the square.
By applying the Pythagorean theorem, we have:
diagonal squared = side squared + side squared
diagonal squared = 122.47 meters squared + 122.47 meters squared
diagonal squared = 15,000 + 15,000
diagonal squared = 30,000
Taking the square root of both sides:
diagonal = √30,000 meters
Calculating the square root of 30,000:
diagonal ≈ 173.21 meters
Therefore, the approximate length of the diagonal of the square field is 173.21 meters.
To find the length of the diagonal of a square field, we need to know the length of one side of the square.
Given that the area of the square field is 3/2 hectares, we can convert this area into square meters in order to find the length of its sides.
1 hectare = 10000 square meters
Therefore, the area of the square field in square meters would be (3/2) * 10000 = 15000 square meters.
Since the area of a square is equal to the square of its side length, we can find the length of one side by taking the square root of the area.
√(15000) ≈ 122.47 meters (rounded to 2 decimal places)
Now that we know the length of one side of the square field, we can use the Pythagorean theorem to find the length of its diagonal.
In a square, the diagonal forms a right triangle with two sides (sides of the square) as legs and the diagonal as the hypotenuse.
Using the formula, a^2 + b^2 = c^2, where a and b are the lengths of the legs (sides of the square), and c is the length of the hypotenuse (diagonal).
Let's call the length of one side "s" and the length of the diagonal "d".
Therefore, we have:
s^2 + s^2 = d^2
2s^2 = d^2
Taking the square root of both sides:
√(2s^2) = √(d^2)
√(2) * s = d
Plugging in the value of the side length:
√(2) * 122.47 ≈ 173.21 meters (rounded to 2 decimal places)
Therefore, the length of the diagonal of the square field is approximately 173.21 meters.
3/2 hectarces = 1500 sq meters
diagnol= side*sqrt2=sqrt(1500) sqrt2
= sqrt(3000) meters= 10sqrt(30) meters