Question 1199156
<br>
Here are the equations you are trying to use to solve the problem:<br>
(1) 37 = x(3x/4)
(2) 37 = y(9y/16)<br>
Those equations both say (incorrectly!) that the length of the diagonal is the product of the length and width.<br>
That of course is not true; the length of the diagonal is found using the Pythagorean Theorem: (length) squared plus (width) squared equals (diagonal) squared.<br>
NOTE: While your textbook suggests using x and (3/4)x for the dimensions of the traditional TV screen, I would prefer to use 4x and 3x -- why introduce fractions into our calculations when not necessary?  I will do that in my response below.<br>
Traditional TV, dimensions 3x and 4x....<br>
The length of the diagonal is 37 inches:<br>
{{{(3x)^2+(4x)^2=37^2}}}
{{{9x^2+16x^2=1369}}}
{{{25x^2=1369}}}
{{{x^2=1089/25=54.76}}}<br>
The area of the screen is<br>
{{{(3x)(4x)=12x^2=12(54.76)=657.12}}}<br>
That matches the answer in your textbook.<br>
LCD TV, dimensions 9x and 16x....<br>
The length of the diagonal is 37 inches:<br>
{{{(9x)^2+(16x)^2=37^2}}}
{{{81x^2+256x^2=37^2}}}
{{{337x^2=1369}}}
{{{x^2=1369/337=4.0623}}} (rounded to 4 decimal places)<br>
The area of the screen is<br>
{{{(9x)(16x)=144x^2=584.97}}} (rounded)<br>
That doesn't quite match what you show as the answer in your textbook.  Perhaps you didn't show the textbook answer correctly...?<br>
The bottom line is that the area of the traditional TV screen is greater.<br>