A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If the field has a length that is twice its width, find the area of the field in square meters.

The area of the rectangular field is 20,000 square meters.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of times a person jogged along the rectangular field = 10

Speed of the person jogging = 12 km per hour

Time he/she jogged = 30 minutes = 0.5 hours

Length of the field = twice its width

2. Find the area of the field in square meters.

Step A: Let's calculate the distance the person jogged

Let's recall the formula of the speed:

Speed = Distance/Time

Distance = Speed * Time

Replacing with the values we know:

Distance = 12 * 0.5

Distance = 6 kilometers

Step B: Let's calculate the perimeter of the rectangular field

Distance jogged = ¨Perimeter * 10

6 kilometers = Perimeter * 10

Perimeter = 6/10

Perimeter = 0.6 kilometers = 0.6 * 1,000 = 600 meters

Perimeter = 2 * Length + 2 * Width

x = Width of the rectangular field

2x = Length of the rectangular field

600 = 2 * 2x + 2 * x

600 = 4x + 2x

600 = 6x

x = 600/6 = 100 meters ⇒ 2x = 200 meters

Step C: Let's calculate the area of the rectangular field

Let's recall the formula of the area of a rectangle:

A = Length * Width

A = 200 * 100

A = 20,000 m² (square meters)