Answer
Height of the screens is $\approx 13.1in$
Work Step by Step
Using the Pythagoras theorem, we can calculate the diagonals of both screens and write them down in term $h$.
Diagonal of first screen:
$=\sqrt{h^2+(1.8h)^2}=\sqrt{h^2+3.24h^2}=\sqrt{4.24h^2}$
Second screen diagonal:
$=\sqrt{h^2+(h+7)^2}=\sqrt{h^2+h^2+14h+49}=\sqrt{2h^2+14h+49}$
As we know, the wider screen has $3in$ wider diagonal, so we can write:
$\sqrt{4.24h^2}=\sqrt{2h^2+14h+49}+3$
To avoid a lot of math/calculation, we can use graphing calculator to find $h$, that is:
$h_1\approx -3.87446$; We can simply cross out this one, as height cannot be negative number.
$h_2\approx 13.12596$
So, the height is $\approx 13.1in$
