Question

1. calculate the length of the diagonal of the state of wyoming.

Explanation:

Step1: Apply Pythagorean theorem

The state of Wyoming is approximated as a rectangle. For a rectangle with length $l = 365$ mi and width $w=275$ mi, the length of the diagonal $d$ can be found using the Pythagorean theorem $d^{2}=l^{2}+w^{2}$.

Step2: Substitute values

Substitute $l = 365$ and $w = 275$ into the formula: $d^{2}=365^{2}+275^{2}$. Calculate $365^{2}=365\times365 = 133225$ and $275^{2}=275\times275=75625$. Then $d^{2}=133225 + 75625=208850$.

Step3: Find the square - root

Take the square - root of both sides to find $d$. So $d=\sqrt{208850}\approx457$ mi.

Answer:

The length of the diagonal of the state of Wyoming is approximately 457 mi.