Chapter 1, Problem 31T

Solution

To find: The largest possible frame width.

The height of the screen is 16.47 inches and width is 29.28 inches.

Given information:

The window frame is,

  

Calculation:

The diagonal given is 32 inches.the screen and it diagonal make right angle triangle as shown in figure. The perpendicular is $9x$ and the base is $16x$

Apply Pythagorean theorem

  ${\left(Hypotenuse\right)}^2={\left(base\right)}^2+{\left(perpendicular\right)}^2$

Substitute the values:

  $\begin{array}{l}{32}^2={\left(9x\right)}^2+{\left(16x\right)}^2\\ 1024=81x^2+256x^2\\ 1024=337x^2\\ x^2=\frac{1024}{337}=3.038\end{array}$

Take square root both sides

  $x=1.83$

Height of the screen= $1.83\times 9=16.47inches$ .

Width of the screen= $1.83\times 16=29.28inches$ .