To find the length of the diagonal of the bedsheet, we can use the Pythagorean theorem.

Let's assume the length of the bedsheet is 'l' and the width is 'w'.

Given that the area of the bedsheet is 120 sq. m, we can write the equation:

l * w = 120

We are also given that the perimeter of the bedsheet is 46 m. Since the perimeter of a rectangle is given by the formula:

2(l + w), we can write the equation:

2(l + w) = 46

Now we have a system of two equations with two variables. We can solve this system to find the values of 'l' and 'w'.

Solving the first equation for 'w', we get:

w = 120 / l

Substituting this value of 'w' into the second equation, we get:

2(l + 120 / l) = 46

Multiplying both sides by 'l' to eliminate the fraction, we get:

2l^2 + 240 = 46l

Rearranging the equation, we get a quadratic equation:

2l^2 - 46l + 240 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation, we get:

(l - 6)(2l - 40) = 0

Setting each factor equal to zero, we get two possible values for 'l':

l - 6 = 0 or 2l - 40 = 0

Solving these equations, we get:

l = 6 or l = 20

Since the length cannot be 6 m (as it would result in a width of 20 m, which is greater than the perimeter), we can conclude that the length of the bedsheet is 20 m.

Now, we can use the Pythagorean theorem to find the length of the diagonal. In a rectangle, the diagonal, length, and width form a right triangle.

Using the formula:

diagonal^2 = length^2 + width^2

We can substitute the values:

diagonal^2 = 20^2 + 120^2
diagonal^2 = 400 + 14400
diagonal^2 = 14800

Taking the square root of both sides, we get:

diagonal ≈ 121.60 m

Rounding to the nearest meter, the length of the diagonal is approximately 122 m, which is not an option given in the answer choices.

Therefore, none of the provided answer choices are correct.

Let the length of the rectangle is L and the breadth of the rectangle is B.