Question

a few days back when samir had fever, he was taken to his uncle's clinic, which is 6 km towards the right of his house, but his uncle was not available, so he was taken to hospital 12 km towards the left. the doctor prescribed him a medicine and the chemist shop was 1 km towards the left. the minimum distance which he had to cover to come back to his home from chemist shop

Answer 1

Let us suppose that Samir house is situated at point A.  His uncle's clinic is at point B.

$Thus, AB = 6$

Now, let us suppose the hospital is at point C and  chemist shop is at D. Hence, we have

$BC=12$

$CD=1$

The minimum distance he will cover to reach is house is AD. So we need to find AD.

Draw a perpendicular line DE. Please see the attached image.

[tex]AE=AB-EB\\ AE=6-1=5\\[/tex]

Now apply Pythagorous theorem in triangle ADE, we have

[tex]AD=\sqrt{12^2+5^2}\\ \\ AD=\sqrt{144+25}\\ \\ AD=\sqrt{169}\\ \\ AD=13[/tex]

Therefore, he had to cover 13 km to come back to his home from chemist shop.