SOLUTION: Open-top box.Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11inch by 14inch sheet of cardboard and folding up the sides.If the area o

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Question 332832: Open-top box.Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11inch by 14inch sheet of cardboard and folding up the sides.If the area of the base is to be 80 square inches, then What size square should be cut from each corner?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Open-top box.Thomas is going to make an open-top box by cutting equal squares
from the four corners of an 11inch by 14inch sheet of cardboard and folding
up the sides.
If the area of the base is to be 80 square inches,
then What size square should be cut from each corner?
:
Let x = side of the removed squares
then
Base dimensions: (11-2x) by (14-2x)
:
Area of base:
(11-2x)*(14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
Arrange as a quadratic equation
4x^2 - 50x + 154 - 80 = 0
4x^2 - 50x + 74 = 0
Simplify, divide by 2
2x^2 - 25x + 37 = 0
use the quadratic formula to find x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in our equation, a=2, b=-25, c= 37
x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2-4%2A2%2A37+%29%29%2F%282%2A2%29+
:
x+=+%2825+%2B-+sqrt%28625-296+%29%29%2F4+
:
x+=+%2825+%2B-+sqrt%28329+%29%29%2F4+
Two solutions
x+=+%2825+%2B+18.138%29%2F4+
x = 43.138%2F4
x = 10.78
and this is the solution that makes sense
x+=+%2825+-+18.138%29%2F4+
x = 6.862%2F4
x = 1.7 inches is the side of the removed squares
:
:
Check by finding the area
(11-2(1.7)) * (14-2(1.7)) = 80.56 ~ 80