SOLUTION: imogen wants to make an open top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard. she figues that for versatility th
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Question 257059: imogen wants to make an open top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard. she figues that for versatility the area of the bottom must be 80 in^2. what size should she cut from each corner
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard.
the area of the bottom must be 80 in^2.
what size should she cut from each corner
:
x = side of the cutout squares
:
The bottom dimensions of the box will be (11-2x) by (14-2x)
;
The area of the bottom given as 80 sq/in, therefore:
;
(11-2x)*(14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
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 solve this:
in this problem a=2; b=-25; c=37
:
:
Two solutions
x =
x = 10.78, obviously, this solution is not valid
and
x =
x = 1.7 inches, the side of the cutout square
:
:
Check solution on a calc
Enter (11 - 2(1.7)) * (14 - 2(1.7)) = 80.56 ~ 80 sq/in
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