The volume of a rectangular box is 120 cubic feet. The length of the box is 2 feet
more than its with its height is one foot less than thrice its width. Find the
dimensions of the box
What method wil heip us answer the problem?
Answers
Given : The volume of a rectangular box is 120 cubic feet.
The length of the box is 2 feet more than its width
its height is one foot less than thrice its width
To find : dimensions of the box
Solution:
Width = b feet
length = b + 2
height = 3b - 1
Volume =
b(b + 2)(3b - 1) = 120
120 = 2 x 2 x 2 x 3 x 5
=> 120 = 8 x 3 x 5
b = 3
b + 2 = 5
3b - 1 = 8
Hence Dimensions of box = 3 , 5 , 8 ft
Other way :
b(b + 2)(3b - 1) = 120
=> b( 3b² + 5b - 2) = 120
=> 3b³ + 5b² - 2b - 120 = 0
(b - 3) (3b² + 14b + 40) = 0
(b - 3) (3b² + 14b + 40) = 0
=> b = 3 , 3b² + 14b + 40 = 0 no real roots
Hence b = 3
Dimensions of box = 3 , 5 , 8 ft
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