The area of a square is 0.5 hectare. The length of its diagonal is
Options a)100m
b)50m
c)250m
Option a)100
Option a)100 m
Length of the diagonal of a square:
d = sqroot ( a^ 2 + a ^ 2 ) = sqroot ( 2 a ^ 2 ) = sqroot ( 2 ) * a
The area of a square is A = a ^ 2
So a = sqroot ( A )
1 hectare = 10,000 m ^ 2
0.5 hectare = 5,000 m ^ 2
a = sqroot ( A ) =
sqroot ( 5,000 ) =
sqroot ( 50 * 100 ) =
sqroot ( 50 ) * sqroot ( 100 ) =
sqroot ( 50 ) * 10 meters
d = sqroot ( 2 ) * a
d = sqroot ( 2 ) * sqroot ( 50 ) * 10 =
sqroot ( 2 * 50 ) * 10 =
sqroot ( 100 ) * 10 =
10 * 10 = 100 meters
To find the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the diagonal forms a right triangle with two sides being the sides of the square. Let's use the length of the side of the square as "s".
According to the problem, the area of the square is 0.5 hectare. One hectare is equal to 10,000 square meters. So, the area of the square is 0.5 x 10,000 = 5,000 square meters.
The formula for the area of a square is A = s^2. Therefore, we can write the equation as:
s^2 = 5,000
To solve for "s", we can take the square root of both sides of the equation:
s = √5,000
Using a calculator, we find that the square root of 5,000 is approximately 70.71 meters.
Now, we can use the Pythagorean theorem to find the length of the diagonal. Let's call the length of the diagonal "d". According to the theorem, we have the equation:
d^2 = s^2 + s^2
Substituting the value of "s" into the equation, we get:
d^2 = 70.71^2 + 70.71^2
Calculating this equation yields:
d^2 = 4,999.99
Taking the square root of both sides, we get:
d ≈ 70.71 meters
Therefore, the length of the diagonal of the square is approximately 70.71 meters.
So, none of the given options (a)100m, b)50m, c)250m) are correct.