Question

A road zig-zags every 100m, first to the East, then to the North ten times. How apart are these two ends?

Answer 1

Given:

Length of each road before it zig-zags = 100 m

Number of tmes = 10

Let's find the distance between the two ends of the roads.

Let's first make a free sketch of the road.

To find the distance between the ends of one zig-zag, apply Pythagoean theorem:

`\begin{gathered} L=√((100*10)^2+(100+10^2)) \\ \\ L=√((1000)^2+(1000)^2) \end{gathered}`

Solving further:

`\begin{gathered} L=√(1000000+1000000) \\ \\ L=√(2000000) \\ \\ L=1414.21\text{ m} \end{gathered}`

Therefore, the distance between both ends is 1414.12 m.

• ANSWER:

1412.12 m