In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 34 inches along the diagonal, what is the screen width?
We can solve this by using the Pythagorean theorem which is below:
[tex]a^2 + b^2 = c^2[/tex]
Or we can say [tex]w^2 + h^2 = d^2[/tex] w = widht h = height d = diagonal measure
With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure. w = don't know yet but need to find h = .75w d = 34 Now lets plugin the information we know into our equation
[tex]w^2 + h^2 = d^2[/tex] [tex]w^2 + (.75w)^2 = 34^2[/tex] Now lets to the math [tex]w^2 + (.75w)^2 = 34^2[/tex] [tex]w^2 + (.75w)^2 = 1156[/tex] [tex]w^2 + .5625w^2 = 1156[/tex] Combine like terms [tex]w^2 + .5625w^2 = 1156[/tex] [tex]1.5625w^2 = 1156[/tex] Divide both sides of the equal sign by 1.5625 [tex]\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}[/tex] [tex]w^2 = 739.84[/tex] Now take the square root on both sides of the equal sign [tex]\sqrt{w^2} = \sqrt{739.84}[/tex] [tex]w = 27.2[/tex]
So the width is 27.2 We can check this by putting 27.2 back into our original equation [tex]w^2 + (.75w)^2 = 34^2[/tex] [tex]27.2^2 + (.75\times 27.2)^2 = 34^2[/tex]
