Question

A rectangular city is 2 miles long and 7 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

√53 ≈ 7.3 miles

Explanation:

The Pythagorean theorem can be used to find the length of a diagonal of a rectangle. The diagonal is effectively the hypotenuse of a right triangle with leg lengths equal to the side lengths of the rectangle.

__

If c represents the distance between opposite corners, and 'a' and 'b' represent the length and width of the city, then we have ...

c² = a² +b²

c² = 2² +7² = 53

c = √53 . . . . . exact corner-corner distance in miles

c ≈ 7.3 . . . . . . approximate corner-corner distance

The exact distance is √53 miles; to the nearest tenth, the distance is approximately 7.3 miles.