Question 948504



{{{drawing(300,300,-3.5,4.5,-1,7,
line(0,0,0,3),line(0,0,-2,1),line(0,0,3,2),
line(-2,1,-2,4),line(3,2,3,5),line(3,5,1,6),
line(-2,4,1,6),line(-2,4,0,3),line(0,3,3,5),
locate(-1.5,0.5,5cm),locate(1.3,1,10cm),locate(0.1,1.7,h)
)}}} 

you are given:
{{{L=10cm}}}
{{{W=5cm}}}
{{{TSA =280cm^2}}}

find:{{{h}}}= height of the cuboid, in cm

recall, the total surface area ({{{TSA}}}) of a cuboid is the sum of the areas of its {{{6}}} faces (and all faces are rectangles) given by:

{{{TSA = 2(LW + Wh + Lh) }}}


{{{280cm^2 = 2 (10cm*5cm + 5cm*h +10cm* h) }}}

{{{280cm^2/2 = 50cm^2 + 5cm*h +10cm* h }}}

{{{140cm^2-50cm^2 = 5cm*h +10cm* h }}}

{{{90cm^2 = (5cm +10cm) h }}}

{{{90cm^2 = (15cm ) h }}}

{{{90cm^cross(2) /15cross(cm) = h }}}

{{{h=6cm  }}}