Question 949644
Assign variables to everything, and use a drawing to help.
x, the side length of the square painting
w, the uniform width around the painting
A, area of frame plus the painting
Given values:
x, unknown
w=2.5 cm
A=3600 square cm


Total Area, {{{(x+2w)^2=A}}}


{{{x^2+4wx+4w^2-A=0}}}
Solving process can continue completely in symbols but easier here to
plug in the given values now.
{{{x^2+4(2.5)x+4(2.5)^2-3600=0}}}
{{{highlight_green(x^2+10x-3575=0)}}}


Discriminant is {{{100+4(3575)=14400=(120)^2}}}


{{{x=(-10+- sqrt(120^2))/2}}}


{{{x=(-10+- 120)/2=highlight_green(-5+- 60)}}}


The MINUS 60 form makes no sense, so use the PLUS form.
{{{highlight(x=55)}}}