Question

A farmer has square field of side length $65$ m. He wants to check all corners of the field. If he starts from one corner and then wants to check its non-adjacent corner then what is the shortest distance covered by the farmer?$(\sqrt{2}=1.414)$

• A. $90.9$ m
• B. $91.91$ m
• C. $9.19$ m
• D. $94$ m

Answer 1

The correct option is B $91.91$ m


Let the corners of field be $A$, $B$, $C$ and $D$ and the farmer start from the corner $A$ the wants to reach the corner $C$ directly by covering the shortest possible distance.

Then he has to follow the path $AC$ as shown in figure,
Now we know that the field is square in shape so all the angles are equal to ${90}^o$.
Now take $△ABC$
applying pythagoras theorem as $AB=BC=65$ m
$A{C}^2=A{B}^2+B{C}^2$
$A{C}^2={65}^2+{65}^2$
$A{C}^2=2\times (65{)}^2$
$AC=\sqrt{2\times (65{)}^2}$
$AC=65\sqrt{2}$ m
$AC=65\times 1.414$
$AC=91.91$ m

shortest distance covered will be $91.91$ m
Hence, option $\left(b\right)$ correct.