If the breadth of a rectangle is decreased by 50%, then to double the area, its length is required to be increased by

### Concept & Area Manipulation To find the required change in one dimension when the other dimension and the total area change, substitute the knowns into the fundamental area formula and solve for the unknown multiplier. $$ L_{new} \times B_{new} = Area_{new} $$ ### Step-by-Step Solution * Let original length = $L$, original breadth = $B$, original area = $LB$. * We want the new area to be double the original: $Area_{new} = 2LB$. * The breadth is decreased by 50%, meaning the new breadth is $0.5B$. * Let the new length be $L_{new}$. Set up the equation: $$ L_{new} \times 0.5B = 2LB $$ * Divide both sides by $B$: $$ L_{new} \times 0.5 = 2L $$ * Solve for $L_{new}$: $$ L_{new} = \frac{2L}{0.5} = 4L $$ * The new length is 4 times the original length. * The required increase is $4L - L = 3L$. * In percentage terms, an increase of $3L$ relative to the base $L$ is $( \frac{3L}{L} ) \times 100 = 300\%$. ### Exam Strategy & Shortcut Use simple numbers. Let initial Area = 100 ($10 \times 10$). Target Area = 200. New breadth = 5 (decreased by 50%). New length required = $200 \div 5 = 40$. The length must go from 10 to 40, an increase of 30. Percentage increase = $(30 \div 10) \times 100 = 300\%$. ### Common Pitfall Mistaking the new value for the increase. Students find that the new length is $400\%$ of the old length and mistakenly choose 400% as the answer, forgetting to subtract the original 100% to find the *increase*. ### Final Answer Therefore, the correct answer is **300%**.