Question : A lawn is in the form of a rectangle having its breadth and length in the ratio $3:4$. The area of the lawn is $\frac{1}{12}$ hectare. The breadth of the lawn is:
Option 1: 25 metres
Option 2: 50 metres
Option 3: 75 metres
Option 4: 100 metres
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Correct Answer: 25 metres
Solution :
Let the length and breadth of a rectangle be $l$ and $b$.
Given that the ratio of the breadth to the length is $3:4$.
$l = \frac{4}{3} × b$____(i)
The area of the lawn $=\frac{1}{12}$ hectare $=\frac{10000}{12}$ m
2
$b × l = \frac{10000}{12}$____(ii)
Solving equation (i) and (ii),
$⇒b × \left(\frac{4}{3}× b\right) = \frac{10000}{12}$
$⇒\frac{4}{3}×b^2 = \frac{10000}{12}$
Solving for $b$,
$⇒b^2 = \frac{10000}{12}×\frac{3}{4}$
$⇒b^2 = \frac{10000}{16}$
$⇒b=\frac{100}{4}$
The breadth of the rectangle $=\frac{1}{4}×100$ = 25 metres
Hence, the correct answer is 25 metres.
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