Answer:
The height of the television is [tex]36.56\ in[/tex]
The width of the television is [tex]16.25\ in[/tex]
Step-by-step explanation:
Let
x-----> the height of a television
y----> the width of a television
we know that
[tex]\frac{x}{y}=\frac{9}{4}[/tex]
[tex]x=\frac{9}{4}y[/tex] -----> equation A
Applying the Pythagoras Theorem
[tex]40^{2}=x^{2}+y^{2}[/tex] -----> equation B
substitute equation A in equation B
[tex]40^{2}=(\frac{9}{4}y)^{2}+y^{2}[/tex]
[tex]1,600=\frac{81}{16}y^{2}+y^{2}[/tex]
[tex]1,600=\frac{97}{16}y^{2}[/tex]
[tex]y^{2}=1,600*16/97[/tex]
[tex]y=16.25\ in[/tex]
[tex]x=\frac{9}{4}(16.25)=36.56\ in[/tex]
