SOLUTION: An open box is to be made from a rectangular piece of tin that is 18 cm wide and 24 cm long be cutting squares of equal size from the four corners and turning up the sides. How lar

Question 181923: An open box is to be made from a rectangular piece of tin that is 18 cm wide and 24 cm long be cutting squares of equal size from the four corners and turning up the sides. How large must a square be cut from each corner if the area of the base of the box is to be 315 sq cm?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The area of the base of the box can be found by multiplying the sides of the base. The sides of the base are equal to the length of the sides of the original rectangular piece of tin less two times the length of the corner pieces (2x). So the area of the base of the box can be expressed as:
Performing the indicated multiplication, we get:
...and this, we are told = 315 sq.cm., so we set these two things equal to get:
Now you subtract 315 from both sides of this equation.
You can solve this quadratic equation using the quadratic formula:
where: a = 4, b = -84, and c = 117, so making the approriate substitutions, we get:

or
or
Now as you can see, if x = 19.5, this would not make any sense because that would mean the cut-out would be larger than the side of the original rectangle! So discard that solution and take the x = 1.5 cm.
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