Answer:
The dimensions are 33.6 and 25.2 inches.
Step-by-step explanation:
Let's say the screen is a rectangle with sides "x" and "y".
We know that x/y = 4/3. So, x = (4/3)y
Since the diagonal is known, we can represent the tv as:
The measures of x and y can be found using the green part of the figure. As we can see, we have a triangle rectangle.
The hypothesis of the triangle is 42 and the sides y and (4/3)y.
Using the Pythagorean Theorem, we know that:
[tex]\text{hyp}^2=a^2+b^2[/tex]
where "hyp" is the hypotenuse and a and b the sides.
So,
[tex]\begin{gathered} 42^2=(\frac{4}{3}y)^2+y^2 \\ 1764=\frac{16}{9}y^2+y^2 \\ 1764=\frac{16y^2+9y^2}{9} \\ 1764=\frac{25y^2}{9} \\ 1764\cdot9=25y^2 \\ \frac{15876}{25}=y^2 \\ y^2=635 \\ y=\pm25.2\text{ } \\ \text{ Since y is a positive a measurement, } \\ y=25.2\text{ inches} \end{gathered}[/tex]
Also, since x = (4/3)y:
[tex]\begin{gathered} x=\frac{4}{3}y \\ x=\frac{4}{3}\cdot25.2 \\ x=33.6\text{ inches} \end{gathered}[/tex]
Thus, the dimensions of the screen are 25.2 and 33.6 inches.
