There is a squared park and a rectangular park in the locality of Pradipbabu. The area of a rectangular park is 78 sq-m less than twice of the area of that square-shaped park whose length is 5 m more than the length of the side of that park and the breadth is 3 m less than the length of the side of that park. Calculate the length of side of the square-shaped park.

Explanation

Let the length of the side of the square-shaped park be x cm.
`:.` Area of park `=x^(2)sq-m`.
As per question, `(x+5)(x-3)=2x^(2)-78`.
or, `x^(2)+5x-3x-15=2x^(2)-78`.
or, `2x^(2)-78-x^(2)-2x+15=0`
or, `x^(2)-2x-63=0" "..........(1)`
Comparing (1) wiht `ax^(2)+bx+c=0` we get, `a=1,b=-2andc=-63`.
`:.` by Sreedhar Acharya's formula we get, `(-(-2)pmsqrt((-2)^(2)-4xx1xx-63))/(2xx1)`
`=(2pmsqrt(4+252))/(2)=(2pmsqrt(256))/(2)=(2pm16)/(2)`
`=(2+16)/(2)` (taking + sign) and `x=(2-16)/(2)` (taking -sign)
`=9andx=-7`
But the length of a side can never be negative, `:.xne-7,` i.e., x=9.
Hence the lengths of the side of the square-shaped park is 9 metres.