Question

The cost of levelling a path of uniform width which surrounds a circular park of diameter 320 m at the rate of Rs. 7.00 per square metre is Rs. 35750. Find the width of the path.

Answer 1

Answer:

1.27m (to 3 significant figures)

Step-by-step explanation:

the diameter of the outside circle can be expressed as 320 + 2x where x = the diameter of the path

therefore the area of the path can be expressed as

$area=(2x+320)^{2} *\pi -320^{2} *\pi$

since we know this area costs Rs. 35750 and the cost per square metre is Rs. 7,

$area=\frac{35750}{7}$

therefore:

$(2x+320)^{2} *\pi -320^{2} *\pi=\frac{35750}{7}$

we can rearrange this to

$x^{2} +320x=\frac{35750}{7}$

which we can solve using the quadratic formula to get 1.2650412066898582...

Hope this helps! Please point out any mistakes so I can correct them.

Answer 2

Step-by-step explanation:

New radius is 160+X

old radius is 160

the difference between them is equal to 35750/7

which has already being given.

compute the arithmetic and we get X=5m which is the required width of the path