Question

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?
[Hint : Let, length = (3x) metres and breadth = (2x) metres. Then, (3x + 5) × 2x = 2600.]

Answer 1

Let the length be $$3x\text{ m}$$ and the breadth be $$2x\text{ m}$$. 

When length is increased by 5 metres, new length $$= (3x + 5)\text{ m}$$. 

According to the problem: $$(3x + 5) \times 2x = 2600$$

$$6x^2 + 10x - 2600 = 0$$ 

Dividing throughout by 2: $$3x^2 + 5x - 1300 = 0$$ 

Factoring: $$3x^2 + 65x - 60x - 1300 = 0$$

$$x(3x + 65) - 20(3x + 65) = 0$$

$$(3x + 65)(x - 20) = 0$$

$$x = -\frac{65}{3} \quad \text{or} \quad x = 20$$ 

Since length cannot be negative, reject $$x = -\frac{65}{3}$$, so $$x = 20$$. 

Breadth of the rectangular field $$= 2x = 2 \times 20 = 40\text{ metres}$$.