A path around the inner side of a rectangular park measuring 37 m $$\times$$​ 30 m occupies 570 m². What is the width of the path?

Correct option is C

​Given:

Dimensions of the park = 37 m × 30 m

Area of the path = 570 m²

Formula Used: 

Area of Rectangle = length $$\times$$​ breadth

​$$\text{Area of outer rectangle} - \text{Area of park} = \text{Area of path}$$​​

​Solution:​

Let width of the path = w

​$$(37 \times 30)-(37 - 2w)(30 - 2w) = 570$$​​

​$$1110-(1110 - 74w - 60w + 4w^2) = 570$$​​

$$4w^2 - 134w + 570 = 0$$ 

​$$2w^2-67w+285=0$$​​

Solving using quadratic formula:

​$$x = \frac{-(-67) \pm \sqrt{(-67)^2 - 4(2)(285)}}{2(2)} \\ \ \\w = \frac{67 \pm \sqrt{4489 - 2280}}{4} \\ \ \\w = \frac{67 \pm \sqrt{2209}}{4} \\ \ \\w = \frac{67 \pm 47}{4} \\ \ \\ w= 28.5 \quad or \quad 5$$

w = 28.5 is not possible not given in the option

w = 5 possible 

Thus, the width of the park is 5 m. 

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