Answer :
[tex]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
[/tex]
By definition, the surface area of a rectangular prism is given by:
[tex]A = 2wl + 2wh + 2hl [/tex]
Where,
w: width of the prism
h: prism height
l: length of the prism
Clearing w we have:
[tex]A = 2 (wl + wh + hl) [/tex]
[tex]A=2w(l + h)+2hl[/tex]
[tex] w=\frac{A - 2hl}{2(l + h)} [/tex]
Substituting values we have:
[tex] w=\frac{208 - 2(8)(6)}{2(6 + 8)} [/tex]
Rewriting:
[tex] w=\frac{208 - 96}{2(14)} [/tex]
[tex] w=\frac{112}{28} [/tex]
[tex]w = 4[/tex]
Answer:
the width of the rectangular prism is:
[tex]w = 4[/tex]
[tex]A = 2wl + 2wh + 2hl [/tex]
Where,
w: width of the prism
h: prism height
l: length of the prism
Clearing w we have:
[tex]A = 2 (wl + wh + hl) [/tex]
[tex]A=2w(l + h)+2hl[/tex]
[tex] w=\frac{A - 2hl}{2(l + h)} [/tex]
Substituting values we have:
[tex] w=\frac{208 - 2(8)(6)}{2(6 + 8)} [/tex]
Rewriting:
[tex] w=\frac{208 - 96}{2(14)} [/tex]
[tex] w=\frac{112}{28} [/tex]
[tex]w = 4[/tex]
Answer:
the width of the rectangular prism is:
[tex]w = 4[/tex]