Question

A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.

Answer 1

Answer:

The exact distance is $\sqrt{109}$ miles.

The distance is approximately 10.4 miles.

Step-by-step explanation:

It is given that a rectangular city is 3 miles long and 10 miles wide. So,

Length = 3 miles

Width = 10 miles

We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.

Using Pythagoras theorem, the length of diagonal is

$d=\sqrt{l^2+w^2}$

where, l is length and w is width.

Substitute l=3 and w=10.

$d=\sqrt{(3)^2+(10)^2}$

$d=\sqrt{9+100}$

$d=\sqrt{109}$

The exact distance is $\sqrt{109}$ miles.

Now,

$d=\sqrt{109}$

$d=10.4403065$

$d\approx 10.4$

The distance is approximately 10.4 miles.