SOLUTION: A rectangular box with a square base is 6 centimeters taller than it is wide. If the surface area of the box is 1710 square centimeters, find the width of the base of the box in ce
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Question 248324: A rectangular box with a square base is 6 centimeters taller than it is wide. If the surface area of the box is 1710 square centimeters, find the width of the base of the box in centimeters. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rectangular box with a square base is 6 centimeters taller than it is wide.
If the surface area of the box is 1710 square centimeters, find the width of the base of the box in centimeters.
:
Let x = side of the square base
then
(x+6) = height of the box
:
Then we know
x^2 = area of top and bottom
x(x+6) = area of the vertical sides
:
area of bottom & top + the area of the 4 vertical sides = surface area
2x^2 + 4x(x+6) = 1710
2x^2 + 4x^2 + 24x = 1710
:
Arrange as a quadratic equation
6x^2 + 24x - 1710 = 0
:
Simplify, divide by 6
x^2 + 4x - 285 = 0
:
Factor to:
(x+19)(x-15) = 0
:
Positive solution
x = 15 cm width of the base
:
:
Check solution by finding the surface area (height = 15 + 6 = 21 cm)
2(15^2) + 4(15*21) =
2(225) + 4(315) =
450 + 1260 = 1710
