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Slavce · Nov 5, 2007, 01:39 PM

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

Please guide me how I should approach this problem.

ebaines · Nov 5, 2007, 01:46 PM

You start with a sheet that's 40 x 30. When you cut out the 4 corners, the dimensions of the base at the center that's left will be (40-2x) by (30-2x). You want that to equal 900, so:

(40-2x) * (30-2x) = 900.

Now multiply this out into the common form for quadratic equations: ax^2 + bx+ c=0, and solve, using the quadratic formula.

Slavce · Nov 5, 2007, 02:05 PM

I got -15 and -20 but in the answers it says 2.3

ebaines · Nov 5, 2007, 02:33 PM

Multiply out the equation I gave you, and you get:

$ 4x^2 -140x+300 = 0 $

Did you get the same thing?

Then divide through by 4 to get:

$ x^2 - 35x + 75=0 $

and solve using the quadratic equation:

$ x = \frac {35 \pm sqrt {35^2 - 4\cdot1\cdot 75}} 2 $

which gives you x = 2.3 or 32.7 Only one of these answers makes sense, so that's the correct one.

terryg752 · Nov 5, 2007, 05:29 PM

Let the side of squares cut = x

Then the base has sides: 40 - 2x and 30 - 2x

Area of base = 900

(40 -2x) (30 - 2x) = 900

1200 - 140 x + 4x^2 = 900

4 x^2 - 140 x +300 = 0

x^2 - 35 x + 75 = 0

Then proceed as usual