Question 6219
Let the length be = L
breadth be = B
as per the question
B*L =120 Sf   eq1
perimeter = 2(L+B) = 46 ft   eq2

again B = 120/L  
put the value of B in eq2 we have
2L+(2*(120/L))=46
or 2L+(240/L)=46
or 2L^2+240 = 46L
or L^2+120 = 23L
or L^2+120 -23L=0

applying the solution of quadratic equation we have
a=1
b=120
c=-23
then applying the solution for quadratic equation we have
{{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

so L = 0.19136150644875 or -120.191361506449
take the positive value of L we have  B= 120/0.19136150644875 =627.28

this seems some thing wrong in question though the solution is here