If length of a rectangle is increased to its three times and breadth is decreased to its half. then the ratio of the area of given rectangle to the area of new rectangle is:

2 : 3

We know that,

Area of rectangle = Length × Breadth

Length = x, Breadth = x

So, according to the question,

New length = 3x

New breadth = \(\frac{1}{2}\)x

Area of the rectangle = 1x × 1x = 1x²

New area of the rectangle = 3x × \(\frac{1}{2}\)x = \(\frac{3}{2}\)x²

Required ratio = 1 x² : \(\frac{3}{2}\)x² = 2 : 3