# Answer to Question #13239 in Geometry for peter sassano

Question #13239

A rectangular prism has a length of 6 inches, a width of 8 inches and a height of 10 inches. Find the surface area and the volume. Then find another rectangular prism with the same area. What is the surface area.

Expert's answer

Surface area S=2*6*8+2*6*10+2*8*10=96+120+160=376 square inches

Volume V=6*8*10=480 cubed inches

Another rectangular prism with the same area:

given - the surface area of the new prism is 376

Let's try to find prism with square base, for example. Let side of the base be x and height of the prism y.

So 2x^2+4xy=376

x^2+2xy=188

x(x+2y)=188=94*2

We can try? for example, x=2

Then x+2y=2+2y=94

2y=92

y=46

Let's verify: S=2*2^2+4*2*46= 376 , so that's it

New prism has square base of side 2 inches& and height of 46 inches. Note, that it's only one of possible variants.

Volume V=6*8*10=480 cubed inches

Another rectangular prism with the same area:

given - the surface area of the new prism is 376

Let's try to find prism with square base, for example. Let side of the base be x and height of the prism y.

So 2x^2+4xy=376

x^2+2xy=188

x(x+2y)=188=94*2

We can try? for example, x=2

Then x+2y=2+2y=94

2y=92

y=46

Let's verify: S=2*2^2+4*2*46= 376 , so that's it

New prism has square base of side 2 inches& and height of 46 inches. Note, that it's only one of possible variants.

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