Answer:
The new frame is 8.3 % bigger.
Step-by-step explanation:
A. Original painting
Let the side of the painting = x.
Then width of frame       = 0.1x
Width of frame + painting  = x + 2×0.1x
Width of frame + painting  = x + 0.2x
Width of frame + painting  = 1.2x
=====
Area of painting        = x²
Area of frame + painting = (1.2x)²
Area of frame          = (1.44x² -x²)
Area of frame          = x²(1.44 - 1)
Area of frame          = 0.44x²
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B. Enlarged painting
         Side of painting = 1.1x
         Width of frame  = 0.1x
Width of frame  + painting = 1.1x+ 0.2x
Width of frame  + painting = 1.3x
=====
       Area of painting = (1.1x)²
       Area of painting = 1.21x²
Area of frame + painting = (1.3x)²
Area of frame + painting = 1.69x²
        Area of frame = 1.69x² - 1.21x²
        Area of frame = (1.69 - 1.21)x²
        Area of frame = 0.48x²
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C. % increase in area of frame
Original area = 0.44x²
  New area = 0.48x²
   Increase = 0.04x²
 % Increase = Increase/Original × 100 %
 % Increase = 0.04x²/0.44x² × 100 %
 % Increase = 0.083 × 100 %
 % Increase = 9.1 %
