Question 33274
Let length of rectangle be L and width be W
given:
L+W = 30cm   which implies W = 30-L
Area = 221 cm
but Area = L*W
L*W  = 30
L(30-L) = 221 
30L - {{{L^2}}} = 221
{{{L^2}}}-30L +221 = 0
{{{L^2}}}-17L-13L+221 = 0
L(L-17)-13(L-17)=0
(L - 13)(L-17)= 0
L = 13 or L = 17
which gives us W = 17 or W = 13
But we are asked to find our the longest side of the rectangle 
so The longest side is 17cm