Question

The length and breadth of rectangular garden of Rehana are 14 meters and 12 meters. If the cost of constructing an equally wide path inside around the garden is 21,380 at the rate of Rs. 20 per sq. meter, then let us write by calculating how much wide is the path​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

The Dimensions of the inner rectangle will be (14 – 2x) × (12 – 2x)

And area of inner rectangular ground = (14 – 2x)(12 – 2x)

Now, area of path = area of the whole garden – an area of the garden without a path

$\frac{cost \: of \: construction}{rate \: of cost \: \: construction} = \: 168 – 168 + 28x + 24x – 4x2$

$⇒ \frac{1380}{20} = 168 – 168 + 28x + 24x – 4x2$

$⇒ 69 = 168 – 168 + 28x + 24x – 4x2$

$⇒ 4x2 – 52x + 69 = 0$

$⇒ 4x2 - 46x – 6x + 69 = 0$

$⇒ 2x(2x – 23) – 3(2x – 23) = 0$

$⇒ (2x – 3)(2x – 23) = 0$

$⇒ 2x – 3 = 0 \:or\: 2x – 23 = 0$

$⇒ x = 1.5 m \:or\: x = 11.5 m$

Now, logically 11.5 m is not possible, because in that case, the length of inner rectangular ground will be negative,

Hence, width of path = x = 1.5 m