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:
\(A = 2 (wl + wh + hl)\)
\(A=2w(l + h)+2hl\)
\(w=\frac{A - 2hl}{2(l + h)}\)
Substituting values we have:
\(w=\frac{208 - 2(8)(6)}{2(6 + 8)}\)
Rewriting:
\(w=\frac{208 - 96}{2(14)}\)
\(w=\frac{112}{28}\)
\(w = 4\)
Answer:
the width of the rectangular prism is:
\(w = 4\)
