SOLUTION: A box with no top is to be constructed from a piece of cardboard whose length measures 17 in. more than its width. The box is formed by cutting squares that measure 5 in. on each s
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Question 1062161: A box with no top is to be constructed from a piece of cardboard whose length measures 17 in. more than its width. The box is formed by cutting squares that measure 5 in. on each side from the four corners and then folding up the sides.
If the volume of the box will be 300 in^3 what are the dimensions of the piece of cardboard?
Found 3 solutions by math_helper, addingup, MathTherapy:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
The 3-dimensional box will be
or
Discard the negative answer.
w = 13 —> l = 13+17 = 30
-
Ans: width is 13in, length is 30in
—
Check:
(13-10)*(30-10)(5) = (3)(20)(5) = 300 (ok)
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
5*w*(w+17) = 300
w(w+17) = 60
w^2+17w = 60
add 289/4 to both sides:
w^2+17w+289/4 = 529/4
Write the left hand side as a square:
(w+17/2)^2 = 529/4
Take the square root of both sides:
w+17/2 = 23/2 or w+17/2 = -23/2
w = 3 or w = -20
discard the -20, we are not looking for a negative number.
Let's try 3 (boy, this is a really narrow box!):
width: 3
Length: 3+17 = 20
height: 5
Volume = w*l*h = 3*20*5 = 300 Correct!
:
John
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
A box with no top is to be constructed from a piece of cardboard whose length measures 17 in. more than its width. The box is formed by cutting squares that measure 5 in. on each side from the four corners and then folding up the sides.
If the volume of the box will be 300 in^3 what are the dimensions of the piece of cardboard?
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