Posted by **Andy G** on Tuesday, January 14, 2014 at 6:29pm.

An open box with a volume of 1500cm^3 is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. Show that this can be done in two different ways, and find exact dimensions of the box in each case.

I have already found the solution using the quadratic equation, can someone help me find the solution using synthetic division?

- Pre-Calc -
**Damon**, Tuesday, January 14, 2014 at 6:59pm
L = 40 - 2x

w = 20 -2x

V = 1500 = L w x

1500= (40-2x)(20-2x)x = (800 -120 x + 4 x^2)x

so

4x^3 - 120 x^2 + 800 x -1500 = 0

make a reasonable guess

x = 5 for example

then the box would be 30*10 * 5 = 1500

good, height of five is a solution

so divide by (x-5)

x^3 - 120 x^2 + 800 x -1500

-----------------------------

(x-5)

= 4 x^2-100 x +300

factor that

4 (x^2- 25 x + 75) = 0

I get about 21 which is too big to take off the width and 2.89

check x = 2.89

20 - 5.78 = 14.22

40 - 5.78 = 34.22

v = 14.22*34.22*2.89 = 1406

well, better do it a bit more accurately

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