Answer to Question #13239 in Geometry for peter sassano

Question

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.

Answer 1

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.