Aroped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of native american artifacts. the combined area of the display and the roped-off is 120 square feet. find the width.

Let
x----------> width a roped off area

we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0

using a graph tool---------> to calculate the quadratic equation
see the attached figure

the solution is 
x=3 ft

the answer is
the width a roped off area is 3 ft