Two straight roads of a well planned colony are perpendicular to each other . There are six parallel lines to road 2 and each lane has 10 houses. Shiva lives in the 7th house of the 6th lane and Rama lives in the 3rd house of the first lane . Find the shortest distance between their hoises

Dear Student,

We can draw the given condition on coordinate axis like the following figure


Here we have 6 parallel lanes which are parallel to X-axis.
each lane contain 10 houses. so we can find the coordinates of each house.

The coordinates of the House of Shiva are (7,6) and house of ram are (3,1). Now we need to find the distance between these two coordinates

Apply distance formula
$$\begin{gathered} D^2={\left(6-1\right)}^2+{\left(7-3\right)}^2 \\ {D}^2={\left(5\right)}^2+{\left(4\right)}^2 \\ {D}^2=25+16 \\ {D}^2=41 \\ D=\sqrt{41} cm \end{gathered}$$

Hence the minimum distance between the two houses will be $\sqrt{41}$
Regards,