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
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-> 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
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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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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.
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.
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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
