Geometry Help

Question

An open box is formed from a rectangular piece of cardboard whose length is 8 cm more than its width by cutting squares whose sides are 2 cm in length from each corner and then folding up the sides. Find the dimensions of the box if its volume is
210 cm3. What is the height width and length?

Answer 1

Let L be length of the box and W the width of the cardboard

length is 8 cm more than its width => L = W + 8

The height of the box is 2 cm, since this represents the squares cut friom the corner.
Let H = 2

The remainder of the cardboard represents the bottom of the box.

The length of the bottom of the box is (L - 4)
The width of the bottom of the box is (W - 4)
4 cm is subtracted because of the two squares cut from the corner.

Volume of the box is V = (L - 4) * (W - 4) * H = 210 cm3

2 * (L - 4) * (W - 4) = 210
(L - 4) *(W - 4) = 105

Since L = W + 8, substitute this into the above equation

(W + 8 - 4) * (W - 4) = 105
(W + 4) * (W - 4) = 105
W² - 16 = 105
W² = 121
W = 11

Since W = 11 cm, then L = 19 cm
The original cardboard has dimensions 19 cm by 11 cm.

The length of the box would (19 - 4) = 15 cm
The width of the box would be (11 - 4) = 7 cm
The height of the box would be 2 cm

Answer 2

 My original answer had some errors.  The other answer is accurate.

Answer 3

L = w + 8   ⇒    w = L - 8

h = 2

v = Lwh = 210

 

L(L-8)2 = 210

 

L² - 8L = 105

 

L² - 8L - 105 = 0

 

(L-15)(L+7) = 0

 

L = 15, -7      -7 NOT VALID

 

w = 15 - 8 = 7

 

h, w, L   =    2, 7, 15