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]
