SOLUTION: The length of a rectangular wood is 5cm more the twice height and its width is five times the height.
What is the dimensions of the wood if its volume is 180cm³?
What is the
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Question 1187757: The length of a rectangular wood is 5cm more the twice height and its width is five times the height.
What is the dimensions of the wood if its volume is 180cm³?
What is the length of the wood if its volume is 495cm³?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!
Let x = height
Then from the given information
2x+5 = length
5x = width
The volume is length times width times height:
V = x(2x+5)(5x)
or
V = 10x^3+25x^2
We are to find x and thus the dimensions if the volume is 180, and if the volume is 495.
One way to find the answers would be to solve the equations 10x^3+25x^2=180 and 10x^3+25x^2=495. But solving a cubic equation is mostly a matter of trial and error.
A much easier method, since the given volumes are whole numbers, is to look for whole number values of x which make the product (x)(2x+5)(5x) equal to 180 or 495.
Clearly x has to be small; so we can just try x=1, 2, 3... to find the answers.
x=1: (x)(2x+5)(5x) = (1)(7)(5) = 35
x=2: (x)(2x+5)(5x) = (2)(9)(10) = 180
x=3: (x)(2x+5)(5x) = (3)(11)(15) = 495
We have found both the required volumes....
ANSWERS:
volume 180 cm^3: dimensions 2cm by 9cm by 10cm
volume 495 cm^3: dimensions 3cm by 11cm by 15cm
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