A park is in the form of a rectangle `120 mx100 mdot` At the centre of the park there is a circular lawn. The area of park excluding lawn is `8700 m^2` . Find the radius of the circular lawn. `(U s epi(22)/7)`

Options

A. `c^(2)`
B. `(c^(2))/(2)`
C. `(c^(2))/(4)`
D. none of these

Answer

C

Explanation

`CD.DE = AD .DB`
But `(AD)/(BD) = (b)/(a)`
`rArr AD = (bc)/(a+b) and DB = (ac)/(a+b)`

`:. CD.DE = (ab)/((a+b)^(2)) c^(2)`
But `c^(2)` is given, so we have to find the maximum value of `(ab)/((a+b^(2))`
Now `(ab)/((a+b)^(2)) = (1)/((a)/(b) + (b)/(a) + 2)`
But `(a)/(b) + (b)/(a) ge 2`
`rArr (a)/(b) + (b)/(a) + 2 ge 4`
`:. (ab)/((a+b)^(2)) le (1)/(4)`
Hence, maximum value of `CD.DE " is " (1)/(4)c^(2)`