Answer:
[tex]5\,(L-10)^2=2000[/tex] is the equation. It agrees with the third option given among the possible answers.
Step-by-step explanation:
If she is using a square piece of cardboard, then have in mind that we are dealing with a square of unknown length "L".
Now, consider that you are removing from each corner of that square a smaller square of surface 5 [tex]in^2[/tex]. Once the small 5 in size square pieces are cut, the four flaps that are left (see attached image) are bent through the lines pictured in grey so they form the final box.
Notice that the dimensions of this box will be:
For the base now we have a smaller square that has length L minus the quantity "two times five" inches.That is: each side of the square base is now L-10 inches long.
Notice as well that the height of the box will be exactly 5 inches (the length of the square cutting).
Therefore, the final volume of the box (which according to the problem should equal 2000 cubic inches) will be given by the product of the box's three dimensions : "L-10" times "L-10" times "5", that is in mathematical terms:
Volume of the box = [tex]Volume=Length\,*\,depth\,*\,height\\2000=(L-10)\,*(L-10)\,*5\\2000= 5\,(L-10)^2[/tex]
which agrees with the third option given among possible answers.
