Question

a path of uniform width of 4 metre runs around and outside a square plot if the area of the path is 288 square metres find the side of a square plot

Answer 1

let be side of outer square=x meter

then side of square=4+x
now, area of square=(4+x)2
288=16+x square+8x
=x square+8x-272

$now \: u \: can \: solve \: by \: splitting \: middle \: term$

Answer 2

Answer:

Side of the square = 12.975 + 4 = 16.975 m

Step-by-step explanation:

Let be side of outer square= x m

side of square = 4 + x

now, area of square = (4 + x) ²

288 = 16 + x ²+ 8 x

x²+8 x-272 = 0

Apply quadratic formula to get value of x

x = - b + √ b² - 4 ac/2 a or - b -√ b² - 4 ac/2 a

x = - 8 + √64 + 1088/ 2 = - 8 + √1152/2 = - 8 + 33.95/2 = 25.95/2 = 12.975

Side of the square = 12.975 + 4 = 16.975 m

or x = - 8 -v 64 + 1088/ 2 ignore negative value as the length can not be negative.