Question

Bob has two way he canto the parkgo he can follow the roads gettingfirst heading south 3.miles, then heading west four miles. The total distance covered following theroads will be 7 miles. The other wayhe can get there is by cutting through some open fields and walk directly tothe park. If we apply Pythagoras's theorem to calculate the distance you will get:

Answer 1

Given:

`\begin{gathered} distance\text{ }heading\text{ }south=3miles \\ distance\text{ }heading\text{ }west=4miles \end{gathered}`

To Determine: The distance if cutting through the field

Solution

The information given can be represented in the diagram below

Note that distance PW in the diagram above is the distance cut through.

The Pythagoras theorem state that in a right-triangle, the square of the hypothenuse is equal to the sum of the squares of the other two sides

From the diagram, the hypothenuse is the PW, the side facing the right angle.

Applying the Pythagoras theorem, we have

`PW^2=3^2+4^2`
`\begin{gathered} PW^2=9+16 \\ PW^2=25 \\ PW=√(25) \\ PW=5miles \end{gathered}`

Hence, the distance cut through is 5 miles