The aspect ratio of a TV screen

Question

1. The aspect ratio of a TV screen is a ratio of the screen's width to the screen's height. Suppose that Noel recycles an old TV screen with an aspect ratio of 4:3. If the TV screen measures 32 inches along its diagonal, what is the perimeter of the screen? Assume that the screen is shaped like a rectangle.
2. 102.4 inches
3. 98.6 inches
4. 76.8 inches
5. 89.6 inches

Answer 1

Use the following formula

P=2l+2 the square root of d2 - l2 where d is the diagonal (given) and l is the length or width (b) in this case

I used 32 for d (given) and 4 for width based on 4:3 ratio given and came up with 71.5 inches

I tried solving this directly using the Pythagorean theorem to determine what c (diagonal) is:

a2 + b2 = c2 =32; but the final answer was not reasonable: 11.3 inches for TV having a diagonal of 32 inches--not physically possible! So always remember to check that your answer is reasonable!

I found this formula online with a google search. I have never seen it before, and that say's alot since I've been tutoring since 1999. Note: it did say the answer was approximated since it has the radical calculation