Question

In a rectangular field Rahim ran diagonally 85 km and when he came back to the rest house by the shorter side of the field which was 13 km , what is the length of the longer side if Rahim had to walk?

• A. 85 km
• B. 34 km
• C. 13 km
• D. 84 km

Answer 1

The correct option is D 84 km

Rahim walks diagonally $85km$ then came back along shorter side by $13km$ .Now this forms a right triangle as shown in the figure.

Applying pythagoras theorem in $△ABC$

${\left(AB\right)}^2{=\left(BC\right)}^2+{\left(AC\right)}^2\Rightarrow {\left(85\right)}^2{=\left(13\right)}^2+{\left(AC\right)}^2\Rightarrow {\left(AC\right)}^2+169=7225\Rightarrow {\left(AC\right)}^2=7225-169=7056\Rightarrow AC=\sqrt{7056}=84$

So the length of longer side is $84km$