# Rectangular box

• Jan 28th 2008, 09:48 PM
sarahh
Rectangular box
A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
• Jan 28th 2008, 10:21 PM
earboth
Quote:

Originally Posted by sarahh
A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?

Let x be the length of one side of one of the squares you have to cut off.

Then you get:

$(20-2x)(30-2x) = 200$ ......... Expand the brackets. You'll get aquadratic equation:

$4x^2-100x+400 = 0$ ......... Solve this equation for x. Only one of the two solutions is valid with your problem.

(For confirmation only: x = 5)
• Jan 28th 2008, 10:59 PM
sarahh
Why do we reject the 20 answer again?
• Jan 29th 2008, 03:24 AM
earboth
Quote:

Originally Posted by sarahh
Why do we reject the 20 answer again?

Plug in the solution into the original equation:

$\begin{array}{ccc}(20-2 \cdot 20)(30-2 \cdot 20)& = &200\\\\ (-20)(-10)&=&200 \end{array}$

That means you cut off more than there exists. In my opinion quite impossible but the modern science ... :D
• Jan 29th 2008, 11:44 AM
sarahh
Ahh that does make sense. Many thanks earboth!
Sarah H.