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 $$m^{2}$$. What is the width of this rectangle?

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

Let's assume the length and width of a rectangle is 3y and 2y respectively.

Initially area = length $$\times$$ width

= $$3y\times2y$$

= $$6y^2$$

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 $$m^{2}$$.

New length = 3y of (100+25)%

= 3y of 125%

= 3.75y

Initially area + 24  = new area

$$6y^2 + 24 = 3.75y\times2y$$

$$6y^2 + 24 = 7.5y^2$$

$$7.5y^2 - 6y^2 = 24$$

$$1.5y^2 = 24$$

$$y^2 = 16$$

y = 4

Width of this rectangle = 2y

= $$2\times4$$

= 8 m