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 think asking google will you get the answer to that question

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.