The diagonal or shortcut that he found represents the hypotenuse of each right angle triangle. The number of blocks he used to walk due due east and north represents the adjacent and opposite sides of the right angle triangle. To determine the number of blocks he would have to walk when he takes the shortcut,d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore
d² = 7² + 3²
d² = 49 + 9 = 58
d = √58
d = 7.6 blocks
The normal distance is
3 + 7 = 10 blocks
The number of blocks by which the shortcut is shorter than walking the blocks is
