<PRE><B>Question 1187757</B>
&lt;br&gt;
Let x = height&lt;br&gt;
Then from the given information&lt;br&gt;
2x+5 = length
5x = width&lt;br&gt;
The volume is length times width times height:&lt;br&gt;
V = x(2x+5)(5x)&lt;br&gt;
or&lt;br&gt;
V = 10x^3+25x^2&lt;br&gt;
We are to find x and thus the dimensions if the volume is 180, and if the volume is 495.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
Clearly x has to be small; so we can just try x=1, 2, 3... to find the answers.&lt;br&gt;
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&lt;br&gt;
We have found both the required volumes....&lt;br&gt;
ANSWERS:
volume 180 cm^3: dimensions 2cm by 9cm by 10cm
volume 495 cm^3: dimensions 3cm by 11cm by 15cm&lt;br&gt;
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