Question: Mark has 42 identical cubes, each with 1-cm edges.He glues them together to form a rectangular solid. Ifthe perimeter of the base is 18 centimeters, find the height of the rectangular solid, in cm.
My solution: I used the equations x + y = 9 derived from 2x+2y = 18, found via perimeter requirements, x*y*h = 42, and the restriction that 42%(x*y)==0.
I made a table that listed possible values of x and y. This included:
There's no need to continue the table for obvious reasons. From here I guessed and checked. The only numbers that followed the restriction 42%(x*y)==0, were x=7 and y=2. From here we know that the height is 3. (42/14 = 3)
My question:The method that I used involves guess and check. While it does solve the problem, I'd prefer a method that doesn't involve guess and check. I know that if I had another equation, I could solve the problem. I also believe there is a way to solve it with matrices. It's been a while since I've had a math class and was looking for either a solution (this isn't a hw problem for me and I already have a working solution) or direction on how to find the third equation.
(Does the third equation involve surface area?)
Thanks!
Edit: Let me know if I need to clarify any part.
My solution: I used the equations x + y = 9 derived from 2x+2y = 18, found via perimeter requirements, x*y*h = 42, and the restriction that 42%(x*y)==0.
I made a table that listed possible values of x and y. This included:
X | Y |
8 | 1 |
7 | 2 |
6 | 3 |
5 | 4 |
There's no need to continue the table for obvious reasons. From here I guessed and checked. The only numbers that followed the restriction 42%(x*y)==0, were x=7 and y=2. From here we know that the height is 3. (42/14 = 3)
My question:The method that I used involves guess and check. While it does solve the problem, I'd prefer a method that doesn't involve guess and check. I know that if I had another equation, I could solve the problem. I also believe there is a way to solve it with matrices. It's been a while since I've had a math class and was looking for either a solution (this isn't a hw problem for me and I already have a working solution) or direction on how to find the third equation.
(Does the third equation involve surface area?)
Thanks!
Edit: Let me know if I need to clarify any part.
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