Question

$\text{The area of a rectangular park is}\frac{8}{35}\text{sq. km.}\text{The length and breadth of the park could be:}$

• A. $\text{Length =}\frac{3}{7}km\text{; Breadth =}\frac{4}{5}km$
• B. $\text{Length =}\frac{4}{7}km\text{; Breadth =}\frac{2}{5}km$
• C. $\text{Length =}\frac{2}{7}km\text{; Breadth =}\frac{2}{5}km$
• D. $\text{Length =}\frac{4}{7}km\text{; Breadth =}\frac{4}{5}km$

Answer 1

The correct option is B $\text{Length =}\frac{4}{7}km\text{; Breadth =}\frac{2}{5}km$

$Case1:$


$\text{Total parts}=35$

$\text{Total area}=1\times 1=1\text{sq. unit}$

$\text{Area of one section}=\frac{1}{35}\text{sq. units}$

$\text{Area of overlapping sections}=\frac{1}{35}\times 16=\frac{16}{35}\text{sq. unit}$

$⟹\text{Area of the park}=\frac{16}{35}\text{sq. km}$

$Case2:$



$\text{Total parts}=35$

$\text{Total area}=1\times 1=1\text{sq. unit}$

$\text{Area of one section}=\frac{1}{35}\text{sq. units}$

$\text{Area of overlapping sections}=\frac{1}{35}\times 8=\frac{8}{35}\text{sq. unit}$

$⟹\text{Area of the park}=\frac{8}{35}\text{sq. km}$

$Case3:$


$\text{Total parts}=35$

$\text{Total area}=1\times 1=1\text{sq. unit}$

$\text{Area of one section}=\frac{1}{35}\text{sq. units}$

$\text{Area of overlapping sections}=\frac{1}{35}\times 4=\frac{4}{35}\text{sq. unit}$

$⟹\text{Area of the park}=\frac{4}{35}\text{sq. km}$

$Case4:$


$\text{Total parts}=35$

$\text{Total area}=1\times 1=1\text{sq. unit}$

$\text{Area of one section}=\frac{1}{35}\text{sq. units}$

$\text{Area of overlapping sections}=\frac{1}{35}\times 12=\frac{12}{35}\text{sq. unit}$

$⟹\text{Area of the park}=\frac{12}{35}\text{sq. km}$

$\text{So, the only case where the total area is}\frac{8}{35}\text{sq. km is in}case2.$

$\therefore \text{The dimensions of the park could be:}$

$\text{Length =}\frac{4}{7}km\text{; Breadth =}\frac{2}{5}km$