The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m². What is the width of this rectangle?

8 m

The ratio of the length to the width of a rectangle is 3 : 2

Let the length = 3x and the breadth = 2x

Then the area = 3x $\times$ 2x = 6x²

According to the question,

If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m² means,

length will be = 125% of 3x = 3.75x

breadth = 2x

Then the area = 3.75x $\times$ 2x = 7.5x²

The increase in area = 7.5x² - 6x² = 1.5x²

1.5x² = 24

x² = 16

x = 4

Then the width of the rectangle = 2x = 2 × 4 = 8 m