SOLUTION: The length is 5 inches more than the width. The width is 3 inches more than the height. The volume is 336 cubic inches. Find the length, width, and height.

Algebra ->  Volume -> SOLUTION: The length is 5 inches more than the width. The width is 3 inches more than the height. The volume is 336 cubic inches. Find the length, width, and height.      Log On


   



Question 1153942: The length is 5 inches more than the width. The width is 3 inches more than the height. The volume is 336 cubic inches. Find the length, width, and height.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

h*(h+3)*((h+3)+5) = 336


h*(h+3)*(h+8) = 336.     (1)


336 = 4*7*12.


It is the decomposition of the number 336 into the product of 3 factors with the same differences 
between the factors as in the formula (1).


Therfore,  x= 4 is the solution for x.


ANSWER.  Height is 4 inches; width is 4+3 = 7 inches;  length is 4+8 = 12 inches.

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the width in inches
+x+%2B+5+ = the length in inches
+x+-+3+ = the height
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+x%2A%28+x+%2B+5+%29%2A%28+x+-+3+%29+=+336+
I tried just plugging in numbers for +x+
+x+=+6+
+6%2A%28+6+%2B+5+%29%2A%28+6+-+3+%29+=+336+
+6%2A11%2A3+=+198+ -not the solution
-----------------
+x+=+7+
+7%2A%28+7+%2B+5+%29%2A%28+7+-+3+%29+=+336+
+7%2A12%2A4+=+336+
+x+=+7+ is the answer
+x+%2B+5+=+12+
+x+-+3+=+4+
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width is 7"
length is 12"
height is 4"
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Here's the plot of the equation of ++y+=+x%2A%28+x%2B5+%29%2A%28+x-3+%29+-+336+