Question

Find the width of a rectangular prism when the surface area is 208 square centimeters -H=8cm,L=6cm

Answer 1

`Area=2area\ of\ base+4\area\ of\ side\\\\ area\ of\ base=2width*L=12width\\\\ area\ of\ side=2width*8+2*6*8=96+16width\\\\ 208=96+16width+12width\\\\ 208=96+28width\ \ \ |Subtract \ 96\\\\112=28width\ \ \ |Divide\ by\ 28\\\\width=4cm`

Answer 2

By definition, the surface area of a rectangular prism is given by:

`A = 2wl + 2wh + 2hl`
Where,
w: width of the prism
h: prism height
l: length of the prism
Clearing w we have:

`A = 2 (wl + wh + hl)`

`A=2w(l + h)+2hl`

`w=(A - 2hl)/(2(l + h))`
Substituting values we have:

`w=(208 - 2(8)(6))/(2(6 + 8))`
Rewriting:

`w=(208 - 96)/(2(14))`

`w=(112)/(28)`

`w = 4`
Answer:
the width of the rectangular prism is:

`w = 4`