SOLUTION: The surface area of a box is 142 square centimeters. The length of the base is 2 centimeters longer than its width. The height of the box is 2 centimeters less than the width o

Question 607574: The surface area of a box is 142 square centimeters. The length of
the base is 2 centimeters longer than its width. The height of the
box is 2 centimeters less than the width of the base. Find the
dimensions of the box.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The surface area of a box is 142 square centimeters.
The length of the base is 2 centimeters longer than its width.
The height of the box is 2 centimeters less than the width of the base.
Find the dimensions of the box.
:
2(L*W) + 2(L*H) + 2(W*H) = 142
Simplify, divide by 2
(L*W) + (L*H) + (W*H) = 71
:
"The length of the base is 2 centimeters longer than its width."
L = (W+2)
:
"The height of the box is 2 centimeters less than the width of the base."
H = (W-2)
:
(L*W) + (L*H) + (W*H) = 71
Replace L & H
W(W+2) + (W+2)(W-2) + W(W-2) = 71
W^2 + 2W + W^2 - 4 + W^2 - 2W = 71
Combine like terms
3W^2 - 4 = 71
3W^2 = 71 + 4
3W^2 = 75
Divide both sides by 3
W^2 = 25
W =
W = 5 cm is the width
then
7 cm is the length
and
3 cm is the height
:
:
See if that checks out
2(7*5) + 2(7*3) + 2(5*3) =
2(35) + 2(21) + 2(15) = 142
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