1. A rectangular piece of land is 100 m long and 7000 cm wide. a) If you run around the piece of land once, calculate how far you would run. b) If you run around the piece of land five times, calculate how far you would run. c) Calculate how many times you must run around the piece of land if you want to run \( 3,4 \mathrm{~km} \) in total.

To solve the problem, we first need to convert all measurements to the same unit. Let's convert the width from centimeters to meters. 1. **Convert the width:** \[ 7000 \text{ cm} = \frac{7000}{100} \text{ m} = 70 \text{ m} \] Now we have a rectangular piece of land that is 100 m long and 70 m wide. ### a) Calculate the distance for one complete lap around the piece of land. The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) \] Substituting the values: \[ P = 2 \times (100 \text{ m} + 70 \text{ m}) = 2 \times 170 \text{ m} = 340 \text{ m} \] So, if you run around the piece of land once, you would run **340 meters**. ### b) Calculate the distance for five laps around the piece of land. To find the distance for five laps, we multiply the perimeter by 5: \[ \text{Distance for 5 laps} = 5 \times P = 5 \times 340 \text{ m} = 1700 \text{ m} \] So, if you run around the piece of land five times, you would run **1700 meters**. ### c) Calculate how many times you must run around the piece of land to run \( 3.4 \text{ km} \). First, convert \( 3.4 \text{ km} \) to meters: \[ 3.4 \text{ km} = 3.4 \times 1000 \text{ m} = 3400 \text{ m} \] Now, to find out how many laps \( n \) you need to run to cover \( 3400 \text{ m} \): \[ n = \frac{\text{Total distance}}{\text{Perimeter}} = \frac{3400 \text{ m}}{340 \text{ m}} = 10 \] So, you must run around the piece of land **10 times** to run \( 3.4 \text{ km} \) in total.