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November 22, 2014

November 22, 2014

Posted by **John** on Tuesday, September 18, 2012 at 8:28am.

A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 420 in^3 when a = 3?

- Math -
**Reiny**, Tuesday, September 18, 2012 at 8:57amYou are cutting out 3-inch squares at the four corners.

Make a diagram.

width of base ---- x inches

length of base --- 2x inches, (you said so)

height of box ---- 3 inches

(x-6)(2x-6)(3) = 420

(x-6)(2x-6) = 140

x^2 - 18x + 36 = 140

2x^2 - 18x - 104 = 0

x = (18 ± √1156)/4

= (18 ± 34)/4

= 13 inches or a negative

so the sheet must have been 13 inches by 26 inches

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