Question 1188209
.
You are designing boxes to ship your newest design. 
You use a rectangular piece of cardboard measuring 40 in. by 30 in. 
to be make an open box with a base (bottom) of 900 in2 by cutting equal squares 
from the four corners and then bending up the sides. 
Find, to the nearest tenth of an inch, the length of the side of the square 
that must be cut from each corner.
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<pre>
Let x be that length of the side of the square to cut from each corner.


Then you get this equation for the box base area


    (40-2x)*(30-2x) = 900  square inches


Simplify and solve (find x)


    1200 - 60x - 80x + 4x^2 = 900

    4x^2 - 140x + 300 = 0

     x^2 - 35x + 75 = 0

     {{{x[1,2]}}} = {{{(35 +- sqrt(35^2 - 4*75))/2}}} = {{{(35 +- sqrt(925))/2}}}.


The only root which suits is  x = {{{(35 - sqrt(925))/2}}} = 2.3 inches (rounded as requested).    <U>ANSWER</U>
</pre>

Solved.


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Closely related lessons to it are the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-of-a-rectangle-surrounded-by-a-strip.lesson>Problems on the area and the dimensions of a rectangle surrounded by a strip</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Cynthia-Besch-and-the-rug.lesson>Cynthia Besch wants to buy a rug for a room</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Making-a-box-from-a-piece-of-cardboard.lesson>Making a box from a piece of cardboard</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Dimensions and the area of rectangles and circles and their elements</U>".


Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.