Question

Rahul walks $ 12 m$ north from his house and turns west to walk $ 35 m$ to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?

Friend’s house Rahul’s house 

Answer 1

As we can see from diagram that Rahul's house is located at point P.

While returning to his home he is following the path RP.

Here

RP is the diagonal of the right-angle triangle PQR.

In triangle PQR

PQ $=12m$

QR $=35m$

Using Pythagoras theorem

$$\begin{gathered} P{R}^2=P{Q}^2+Q{R}^2 \\ \Rightarrow P{R}^2={12}^2+{35}^2=144+1225=1369 \\ \Rightarrow PR=\sqrt{1369}=37m \end{gathered}$$

Hence, he needs to walk $37m$ while returning from his friend's house.