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Question

A picture frame has an overall area of 96 square inches and a length of 12 inches. When designing how thick to make the frame the engineers decided that they wanted the inside area (glass) to be 60 square inches. How many inches thick does the fame need to be?

Answer 1

frame is 12 by 90/12 = 7.5

the frame is 12 by 7.5 inches

96-60 = 36 inches for the area of the frame alone

x = thickness of the frame

(12-2x)x + (7.5-x)x + 4x^2 = 36

12x -2x^2 + 7.5x -x^2 +4x^2 =36

x^2 +19.5x -36 = 0

x = -19.5/2 + or - (1/2)sqr(19.5^2 +4(36)

=-9.75 + or - (1/2)sqr(380.25+144)

=-9.75 + or - (1/2)sqr(525.25)

=-9.75 + or - 11.46 = about 1.71 inches thick (ignore the negative square root)