Answer:
121 sq. in
Step-by-step explanation:
area of the frame = 48 square inches
if [tex]x[/tex] is the side length of the square, then ([tex]x[/tex] + 2) is the side length of the square after the frame has been added.
the area of the picture + the frame is:
([tex]x[/tex] + 2) ([tex]x[/tex] + 2)
the area of just the frame is given by ([tex]x[/tex] + 2) ([tex]x[/tex] + 2) - [tex]x[/tex] x [tex]x[/tex]:
([tex]x[/tex] + 2) ([tex]x[/tex] + 2) - [tex]x[/tex] x [tex]x[/tex] =48
[tex]x[/tex]²+ [tex]x[/tex] x 2 + 2 x [tex]x[/tex] + 2 x 2-[tex]x[/tex]² = 48
[tex]x[/tex]² + 2[tex]x[/tex] + 2[tex]x[/tex] + 4-[tex]x[/tex]² = 48
4[tex]x[/tex] + 4 = 48
then subtract 4 from both sides:
4x = 44
and divide both sides by 4:
x = 11
the area of the square is 11 (11) = 121.
i think this is correct?
hope this helps :))
