Apainting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. the painting was enlarged by 10%. by what percent is the new frame bigger than the original frame if the width of the frame remains the same?

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

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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

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             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 %

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step-by-step explanation:

when the line is solid:

when the line is dashed:

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this < inequality sign means:

about the problem:

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