Let original length = 100 and original breadth = 100

Then original area = 100 × 100 = 10000

Length of the rectangle is halved

=> New length = $\dfrac{\text{Original length}}{2}=\dfrac{100}{2}=50$

Breadth is tripled

=> New breadth= Original breadth × 3 = 100 × 3 = 300

New area = 50 × 300 = 15000

Increase in area = New Area - Original Area = 15000 - 10000= 5000

Percentage of Increase in area = $\dfrac{\text{Increase in Area}}{\text{Original Area}} \times 100$

$=\dfrac{5000}{10000} \times 100=50\% $