<p>To make a cardboard table for her dollhouse, Ouisie uses a rectangular piece of cardboard measuring 40 inches wide and 60 inches long. She cuts four equal-sized squares from each corner and folds down the sides at a 90º angle. If the top of the table measures 800 square inches, how tall, in inches, is the table?
(A) 40
(B) 30
(C) 25
(D) 20
(E) 10</p>
<p>I got the height of the table as 10.
Don’t let the question intimidate you, it is just basic thinking in geometry and then algerbra.
Now, if you cut a corner out of each corner of a cardboard sheet, you open up the space for folding it, creating the table in this question.
Lets call the side length of the square she cuts x. Each side is going to be reduced by 2 x. So the sides go from 40 x 60 when it is a sheet, to (40 - 2x)(60 - 2x) for the upright portion when it is a table. All you have to do is set that expression equal to 800 and solve for x.
(40 - 2x)(60 - 2x) = 800
2400 - 120x - 80x + 4x^2 = 800
4x^2 - 200x + 2400 = 800
4x^2 - 200x + 1600 = 0
x^2 - 50x + 400 = 0
(x - 40)(x - 10) = 0
x = 40 and x = 10</p>
<p>Now we can’t have 2 answers, and indeed, x = 40 is an extraneous solution. The expression (40 - 2x) represents the smaller side on the upright table, and 40 - 2x is -40! We can’t have a side with a negative length x= 10.</p>
<p>Now, in this case they made it nice. X, or the amount she cut into each corner is also the height in the final table. But in this type of question, make sure you are answering what it asks for (it could ask the lengths of one of the sides instead). So the answer is 10.</p>
<p>I hope I did that right, and that it helped. Let me know if you need me to elaborate on any part.</p>
<p>I agree with Apprentice. Since they explained it so well, and I don’t have much to add, here’s a picture that I doodled on paint.
<a href=“http://img825.imageshack.us/img825/7538/tablex.png[/img]”>http://img825.imageshack.us/img825/7538/tablex.png
![http://img825.imageshack.us/img825/7538/tablex.png[/img]](http://img825.imageshack.us/img825/7538/tablex.png%5B/img%5D){kind=link}
</a></p>
<p>^hahahahaha</p>
<p>nice explanation apprentice and i liked the drawing bsmith lol, i should have drew a pic</p>
<p>You’re welcome.</p>
<p>Also, I realized this question is an excellent example of how to do better even if you don’t know the answer, by checking if the answer is reasonable.</p>
<p>if you can realize that the shorter upright side at the end is going to be 40 - 2x, this gives you your answer off the bat.
(A) 40
(B) 30
(C) 25
(D) 20
(E) 10 </p>
<p>Everything except D and E will give you a negative value for the side, and D will give you a value of 0 for the side, E stands out as the only reasonable answer.</p>