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A man goes 10 m due south and then 24 m due west. How far is he from the starting point?

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20 m

23 m

26 m

24 m

answer is C.

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Detailed Solution

Given,
A man goes 10 m due south and then 24 m due west.
Consider the figure,
The Pythagoras Theorem is given as,

H y p o t e n u s e 2 = B a s e 2 + P e r p e n d i c u l a r 2

Using the Pythagoras theorem.
Then,

A C 2 + A B 2 = B C 2

From data,
AC=24m
AB=10m
Therefore,

{AC}^{2} + A B^{2} = B C^{2}

\Rightarrow {(24)}^{2} + {(10)}^{2} = B C^{2}

\Rightarrow B C^{2} = 576 + 100

\Rightarrow B C^{2} = 676

\Rightarrow BC = 26 m

The man is

26

m far from the starting point.
Hence, option 3 is correct.

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