Noam walks home from school by walking 8 blocks north and then 6 blocks east. how
much shorter would his walk be if there were a direct path from the school to his house?
assume that the blocks are square.

4 blocks shorter.

Step-by-step explanation:

Noam walks home from school by walking 8 blocks north and then 6 blocks east.

If Noam walks 8 blocks from School at A towards north to the point B and then from B towards east by 6 blocks to reach home at C, then Δ ABC will form a right triangle whose sides with 90° are AB = 8 blocks and BC = 6 blocks and AC is the hypotenuse which is given by

AC² = AB² + BC² = 8² + 6² = 100

⇒ AC = 10 blocks.

So, total distance that Noam travels is (8 + 6) = 14 blocks.

And if he walks along AC, then the distance will be 10 blocks which is (14 - 10 ) = 4 blocks shorter than his actual path. (Answer)