Q7 of 99 Page 264

The length and breadth of rectangular garden of Rehana are 14 meter and 12 meter. If the cost of constructing an equally wide path inside around the garden is Rs. 1,380 at the rate of Rs. 20 per sq. meter, then let us write by calculating how much wide is the path.

We know, area of rectangle = length × breadth


Area of outer rectangle = 14m × 12m = 168m2


Let the width of path be ‘x’ m.



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


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


Now, area of path = area of whole garden – area of garden without path


Area of path


⇒ 69 = 168 – (14 – 2x)(12 – 2x)


⇒ 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


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