The ratio between the length and the breadth of a rectangular field is 3 : 2. If only the length is increased by 5 metres, the new area of the field will be 2600 sq. metres. What is the breadth of the rectangular field ?

Given,

The ratio between the length and the breadth of a rectangular field is 3 : 2.

Let length of rectangle be 3x and breadth of rectangle be 2x.

Given,

When the length is increased by 5, new length = 3x + 5.

Area of rectangle with increased length = 2600 m²

By formula,

Area of rectangle = length × breadth

⇒ 2600 = (3x + 5)(2x)

⇒ 2600 = 6x² + 10x

⇒ 6x² + 10x - 2600 = 0

⇒ 2(3x² + 5x - 1300) = 0

⇒ 3x² + 5x - 1300 = 0

⇒ 3x² + 65x - 60x - 1300 = 0

⇒ x(3x + 65) - 20(3x + 65) = 0

⇒ (x - 20)(3x + 65) = 0

⇒ (x - 20) = 0 or (3x + 65) = 0     [Using zero-product rule]

⇒ x = 20 or x = $-\dfrac{65}{3}$

Since, length cannot be negative.

Thus, x = 20.

Breadth of rectangle = 2x = 2 × 20 = 40 m.

Hence, breadth of rectangle = 40 m.