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A portrait has dimensions of 50 inches by 60 inches and is surrounded by a frame of uniform width. If the total area (portrait plus frame) is 3456 square inches, find the width of the frame

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sqdancefan

Answer:

  2 inches

Step-by-step explanation:

If x is the width of the frame, then the overall dimensions are ...

  (50 +2x) by (60 +2x)

so the area is ...

  3456 = (50 +2x)(60+2x)

  x^2 +55x -114 = 0 . . . . . . . divide by 4, subtract the left side

  (x +57)(x -2) = 0 . . . . . . . . . factor

Solutions to this are x=2 and x=57 (extraneous).

The width of the frame is 2 inches.

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