Sandy purchases an entertianment center on clearance at 65% off that has an opening measuring 42 inches by 20.5 inches. If widescreen televisions (16:9 aspect ratio) are on sale at the local electronics store for the next 3 days, what is the maximum screen size that Sandy should purchase, assuming that each screen has a 1 inch wide frame bordering the screen.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Let `d` be diagonal and `a` and `b` sides of TV. By Pythagorean theorem

`d=sqrt(a^2+b^2)`

Also since `a:b=16:9` it follows `a=16/9b`and `b=9/16a` hence

`d=sqrt((16/9b)^2+b^2)=sqrt(337)/9b`                                    (1)

So if we put `b=18.5` (we subtract 1in from both sides for the frame) we will get upper bound on TV diagonal

`d leq sqrt(337)/9 cdot 18.5 approx 37.73`                                         (2)

Since `b=9/16a` we can write (1) as

`d=sqrt(337)/16a`

Now to get upper bound on `d` we put `a=40`

`d leq sqrt(337)/16 cdot40 approx 45.89`                                           (3)

Now taking both (2) and (3) into account we see that maximum size of TV diagonal is 37.73 in.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial