The area of the bottom of a rectangular box is 316cm squared the area of one side is 168cm squared and the area of the other is 120cm squared. What are the dimensions of the box?

Answers

Answered by Steve
If the box's dimensions are x,y,z, then we have

xy = 316
xz = 168
yz = 120

Hmmm. Really? I suspect a typo, since the dimensions are not integers.

316 = 2^2 79
168 = 2^3 3 7
120 = 2^3 3 5

That 79 is a problem.
Answered by MathMate
Let h=height of the box.
Then
width=120/h
length=168/h

We know the area of the base is
Ab=316

so Ab=width*length, or
316=(120/h)*(168/h)=(120*168)/h².
Solve for h
h=√(316/(120*168)
=12√35/√79.
Use the above equations above to find length and width.

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