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A rectangle piece of tin 40 cm by 30 cm is to be made into an open box with a base of 900cm2 by cutting equal squares from the hour corners and then bending up the sides. Find, to the nearest tenth of a centimetre the length of the side of the square cut from each corner.

The squares would have a side of length x, and there are two squares (one at each end)

on each side. The area of the base is then (40-2x)(30-2x), and that is suppose to be 900.

Multiplying out the area gives 4x² - 140x + 1200.

Setting that to 900 gives 4x² - 140x + 1200 = 900.

Subtracting 900 from both sides gives 4x² - 140x + 300 = 0.

Dividing the equation by 4 gives x² - 35x + 75 = 0.

Putting this equation in Excel lets x be estimated to be 2.3,

so each square should be 2.3 x 2.3.

Algebra

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