Question 1009273
w for width, y for height;
Express the ratios as  w/y for "width to height".  This is  {{{16/9}}}.  Further,  {{{w/y=16/9}}} applies to each of the TVs.


Each TV can be cut along a diagonal to form two right triangles, of legs w and y, and the diagonal is hypotenuse.


The 42 inch,  $420 TV
{{{system(w^2+y^2=42^2,w/y=16/9)}}}
{{{system(w^2+y^2=42^2,w=16y/9)}}}
{{{(16y/9)^2+y^2=42^2}}}
{{{y^2(16/9+1)^2=42^2}}}
{{{(25/9)^2*y^2=42^2}}}
{{{y^2=(9/25)^2*42^2}}}
{{{y=(9*42)/25}}}
{{{highlight(y=225/42)}}}
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Use the aspect ratio again.
{{{w=(16/9)*y}}}
{{{w=(16/9)(225/42)}}}
{{{w=16*25/42}}}
{{{w=8*25/21}}}
{{{w=200/21}}}
{{{highlight(w=200/21)}}}
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The area for this TV screen is  {{{w*y=(200/21)(225/42)=(100*225)/(21*21)}}}
{{{wy=22500/21^2}}}
{{{highlight(wy=51.02)}}} square inches
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The cost per square inch is  {{{420/51.02=highlight(highlight(8.23(dollars/squareInch)))}}}.



The 50 inch, $550 TV
Can you do this one?