Use Lagrange multipliers to find the dimensions of a rectangular box with largest volume if the total surface area is given as 400 cm2. (Enter the dimensions (in centimeters) as a comma separated list.)

The dimension of the given box is by by.

Step-by-step explanation:

Assume the dimension of the box is x by y by z.

Total surface area of the box= 2xy+2yz+2xz=400

The volume of the box is f(x,y,z)= xyz

To maximum volume under constrain,

g(x,y,z)=2xy+2yz+2xz-400=0

we use Langrange Multiplier.

Assume that,

If ,

This implies that, x=y=z

Then 2xy+2yz+2xz=400

⇒xy+yz+xz=200

⇒x²+x²+x²=200

⇒3x²=200

Therefore cm.

i got 86 for this

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option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have