Answer:
The width of the border is 1.5 units
Step-by-step explanation:
Let
x -----> the width of the border
we know that
The combined area of picture plus frame is 180 square units
so
[tex]180=(9+2x)(12+2x)[/tex]
Apply distributive property
[tex]180=(9+2x)(12+2x)\\\\180=108+18x+24x+4x^{2} \\\\4x^{2}+42x-72=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
the solution is x=1.5 units
Remember that the width cannot be a negative number
see the attached figure
