Question 325506
If the sides of a square are lengthened by 3 km, the area becomes 81 square kilometers.Find the length of the original square


Let one side of original square be S


Since a side of the new, lengthened square is 3 km greater than one side of the original square, then one side of the new, lengthened square is S + 3


Since the new, lengthened square has an area of 81 sq. km, then we'll have:
{{{(S + 3)^2 = 81}}}


(S + 3)(S + 3) = 81


{{{S^2 + 6S + 9 = 81}}}


{{{S^2 + 6S - 72 = 0}}}


(S + 12)(S - 6) = 0


Therefore, S, or one side of original square is either -12, or 6, but since we CANNOT have a negative measurement, we IGNORE S = - 12, which leaves one side of the original square: {{{highlight_green(6)}}} km.