One of the sides of a rectangular field is 30 m. Half of the field is sown with oats, and the other half with wheat and rye.

One of the sides of a rectangular field is 30 m. Half of the field is sown with oats, and the other half with wheat and rye. Wheat occupies 600 square meters, and rye occupies one sixth of the entire field. How long should the fence be around the entire field?

We take the area of the entire field as x, therefore:

sown oats x / 2 sq. m;

wheat sown 600 sq. m;

rye sown x / 6 sq. m.

Let’s make the equation:

x = 600 + x / 2 + x / 6;

We solve the equation:

x = 600 + 3x / 6 + x / 6;

x = 600 + 4x / 6;

x = 600 + 2x / 3;

x – 2x / 3 = 600;

(3x – 2x) / 3 = 600;

x / 3 = 600;

x = 1800 sq. m.

The area of the entire field is 1800 sq. m. One of the sides of the rectangular field is 30 meters, therefore the second – 1800/30 = 60 square meters. m.

The length of the fence is equal to the perimeter of the field, we calculate:

30 * 2 + 60 * 2 = 60 + 120 = 180 (m).

Answer: the fence that encloses the entire field should be 180 meters long.