The library in Ben's town is 3 blocks east and 7 blocks north of his house. He finds a short cut by walking diagonally from his house to the library. How much shorter is the shortcut than walking the blocks?

The answer to your question is 2.4 units shorter.

Step-by-step explanation:

Data

3 blocks east and 7 blocks north.

Process

1. - Calculate the distance walking the blocks

distance = 3 + 7

distance = 10

2. - Calculate when walking diagonally using the pythagorean theorem

distance² = 3² + 7²

distance² = 9 + 49

distance² = 58

distance = 7.62

3. - Calculate the difference of distances

Δd = 10 - 7.62

Δd = 2.38 units

Step-by-step explanation:

A right angle triangle is formed.

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

10 - 7.6 = 2.4