Question 987761
.
42-inch television has the aspect ratio of  16:9. 


It means that &nbsp;{{{x/y}}} = {{{16/9}}}, &nbsp;where &nbsp;<B>x</B>&nbsp; and &nbsp;<B>y</B>&nbsp; are measures of the &nbsp;TV screen in horizontal and vertical directions respectively, &nbsp;in inches. 


Hence, &nbsp;x = {{{16/9}}}{{{y}}}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)


In addition, &nbsp;by the Pythagorean theorem, &nbsp;{{{x^2}}} + {{{y^2}}} = {{{42^2}}}.


Substitute &nbsp;(1)&nbsp; here. &nbsp;You will get


{{{16^2/9^2*y^2}}} + {{{y^2}}} = {{{42^2}}},


{{{256*y^2}}} + {{{81*y^2}}} = {{{42^2*81}}},


{{{337*y^2}}} = {{{142884}}},


y = {{{sqrt(142884/337)}}} = 20.591 inches (approximately).


Hence, &nbsp;x = {{{16/9}}}{{{y}}} = {{{16/9}}}.{{{20.591}}} = 36.606 inches.


Now you know the dimensions of the TV set: &nbsp;36.606 in &nbsp;horizontally and &nbsp;20.591 in&nbsp; vertically. 


This is how to start the solution.