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:
 $A = 2 (wl + wh + hl)$
 $A=2w(l + h)+2hl$
 $w=\frac{A - 2hl}{2(l + h)}$
 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:
 $w = 4$