The top of a rectangular box has an area of 63cm2. Its side has an area of 42 cm2 and its end has an area of 54 cm2. What are the dimensions of the box?

Question

anonymous · Answer

What do you mean by side and end?

anonymous · Answer

The question came right from the book. I am not sure

directrix · Answer

6 by 7 by 9, perhaps?

anonymous · Answer

can you please show me how you got the answer

anonymous · Answer

Well I'll assume that the side refers to the smallest face of box and end refers to the second largest face, and the top is the largest face. If we make a box and label the sides x, y, z like this:

 

We know xy = 54 xz = 42 yz = 63 rearranging the second equation gives x = 42/z and rearranging the third equation gives y = 63/z --> We plug in these values of x and y in to the first equation and solve for z.
 (63/z) * (42/z) = 54 
2646/z^2 = 54 
z^2 = 2646/54 
z ^2 = 49 
     z =  7--> Now that we know z, we can plug it in to the other equations and solve for x and y. x(7) = 42 --> x = 6  y(7) = 63 --> y = 9  Therefore, the dimensions of the box are x = 6 , y = 9 , z = 7 or 6  * 9  * 7 are the dimensions.

anonymous · Answer

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