Final answer:
The diagonal route across the field is 216.27m long, while the route around the edge is 600m long. Therefore, the diagonal route is shorter by approximately 383.73m.
Step-by-step explanation:
To find out how much shorter the diagonal route is compared to walking around the edge of the field, we can calculate the lengths of both routes and find the difference. Let's start by finding the length of the diagonal route using the Pythagorean theorem. The diagonal forms a right triangle with the sides of the field as its legs. The length of the diagonal (d) can be found using the formula d = sqrt(a^2 + b^2), where a and b are the lengths of the sides of the field.
In this case, a = 120m and b = 180m. Plugging these values into the formula gives us d = sqrt(120^2 + 180^2) = sqrt(14400 + 32400) = sqrt(46800) ≈ 216.27m.
Now, let's calculate the length of the route around the edge of the field. Since the field is rectangular, the distance around the edge can be found by adding the lengths of all four sides. The length of each side is given, so we can calculate the total distance by using the formula (2 × length) + (2 × width).
In this case, the length is 120m and the width is 180m. Plugging these values into the formula gives us (2 × 120) + (2 × 180) = 240 + 360 = 600m.
Finally, we can find the difference between the two routes by subtracting the length of the diagonal route from the length of the route around the edge. The difference is 600m - 216.27m = 383.73m.