Question

You practice on a soccer field that is in the shape of a rectangle. It is 105 meters long by 68 meters wide. Your coach makes you run the diagonal across the field. About how far do you have to run

Answer 1

To find the distance of the diagonal of a rectangle, you can use the Pythagorean theorem. In this case, the diagonal of the soccer field is approximately 125.09 meters.

Step-by-step explanation:

To find the distance of the diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the rectangle is 105 meters and the width is 68 meters. So, we can consider the length and width as the two sides of a right triangle, and the diagonal as the hypotenuse.

Applying the Pythagorean theorem, we have:

`a^2 + b^2 = c^2`

`105^2 + 68^2 = c^2`

`11025 + 4624 = c^2`

`15649 = c^2`

`c = \sqrt{15649`

c ≈ 125.09 meters

Answer 2

To find the distance run diagonally across a soccer field, use the Pythagorean theorem. The field's diagonal is calculated as the hypotenuse of a right-angled triangle formed by the field's length and width, resulting in approximately 125 meters.

Step-by-step explanation:

To calculate the distance your coach makes you run across the diagonal of a soccer field that is 105 meters long and 68 meters wide, you would use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the diagonal acts as the hypotenuse of a right-angled triangle whose sides are the lengths and the widths of the field.

Step-by-step calculation:

1. Write down the dimensions of the field: length (l) = 105 meters, width (w) = 68 meters.
2. Apply the Pythagorean theorem: (Diagonal)2 = (length)2 + (width)2.
3. Substitute the known values: (Diagonal)2 = (105)2 + (68)2.
4. Calculate the squares: (Diagonal)2 = 11025 + 4624.
5. Add the squares: (Diagonal)2 = 15649.
6. Take the square root to find the diagonal: Diagonal = √15649.
7. Calculate the square root: Diagonal ≈ 125 meters.

The approximate diagonal distance you have to run is 125 meters.