SOLUTION: 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 cu

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.

Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Draw this helps
the bottom will be 40-2x by 30-2x, and that will equal 900 in^2. x is the length of the side of the square.
1200-140x+4x^2=900
4x^2-140x+300=0
x^2-35x+75=0
x=(1/2)(35+/- sqrt (1225-300)); sqrt 925=30.4
x=32.7 inches and 2.3 inches; 2.3 inches is the answer.
the sides will become 35.4 x 25.4=899.16 in^2.

Answer by ikleyn(53765)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~

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 = = . The only root which suits is x = = 2.3 inches (rounded as requested). ANSWER

Solved.

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Closely related lessons to it are the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
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    - Making a box from a piece of cardboard
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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

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.

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