Question

A lemming sits at a corner of a square with side length $10$ meters. The lemming runs $6.2$ meters along a diagonal toward the opposite corner. It stops, makes a $90^{\circ}$ right turn and runs $2$ more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?

$2$

$4.5$

$5$

$6.2$

$7$

Solution:

Based on the lengths given in the problem, the lemming is still in the square after it stops.

Since the lemming is still in the square, the sum of the distances to the horizontal sides is $10$ meters and the same for the vertical sides. Therefore, the $4$ distances sum to $20$ meters, making the average $20 \div 4 = 5$ meters.

Thus, C is the correct answer.

2007 AMC 8 Problem 22

Solution:

Problem 22 in Other Years