Question

Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot. 40 feet 80 feet 117 feet 160 feet

Answer 1

Alice and Amy are standing on the 2 opposite endpoints of the diagonal of a rectangle. (Well, this is the best way to think of the situation geometrically.)

The shortest distance is certainly when Amy walks straight through the diagonal. So, we need to find the length of the diagonal.

A diagonal divides a rectangle into 2 congruent (identical) right triangles. The sides of any of these 2 triangles are 100 ft and 60 ft, thus we can find the diagonal by the Pythagorean theorem:

$|Diagonal|^2=100^2+60^2=10,000+3,600=13,600$, 

so, 

$|Diagonal|= \sqrt{16,600}\approx117$ (ft).


Answer: 117 ft