Question

1. a soccer field is a rectangle 100 meters wide and 130 meters long. the coach asks players to run from one corner to the other corner diagonally across. what is that distance?

Explanation:

Step1: Apply Pythagorean theorem

The diagonal $d$ of a rectangle satisfies $d^2 = l^2 + w^2$, where $l=130$ m (length) and $w=100$ m (width).
$$d^2 = 130^2 + 100^2$$

Step2: Calculate squared values

Compute the squares of length and width.
$$d^2 = 16900 + 10000$$

Step3: Sum the squared values

Add the two results from Step2.
$$d^2 = 26900$$

Step4: Solve for diagonal distance

Take the square root to find $d$.
$$d = \sqrt{26900} = 10\sqrt{269} \approx 164.01$$

Answer:

The diagonal distance is $\boldsymbol{10\sqrt{269}}$ meters, or approximately 164 meters.