The aspect ratio (length to width) of an LCD computer monitor is 5 : 4.

Question

The aspect ratio (length to width) of an LCD
computer monitor is 5 : 4. The LCD monitor of
a Toshiba laptop computer has a perimeter of
32.4 inches. What is the diagonal measure of
the screen. Round your answer to the nearest
thousandth of an inch?

Answer 1

The formula for the Perimeter P is Width+Height+Width+Height
     P = 2W+2H   

     2W + 2H = 32.4    (eq1)

The aspect ratio of 5:4 means that:  W/H = 5/4

     or   W = (5/4)H

           4W - 5H = 0        (eq2)

 

Also, we will use the Pythagorean Theorem:     a²+b²=c²      or  W²+ H² = D²

 O.K., now the easy math:

Let's determine W and H.

    2W   +  2H   = 32.4      (eq1 again)

    4W   +  4H   =  64.8         (2*eq1)

    4W   -   5H   =    0              (eq2)

 ---------------------------     (elimination method; subtract the two equations)

                9H  =  64.8

                  H = 7.2

              2H = 14.4

     2W + 2H = 32.4    (eq1 again)
 ------------------------     (elimination method; subtract top equation from bottom)

     2W         =  18.0

          W = 9.0

 

Checking (very important):

  Is  2*(9.0)+2*(7.2) = 32.4   ?

          18.0 + 14.4  = 32.4   ?

             32.4 = 32.4   ? yes

  Is  9.0/7.2  =  5/4   ?

         5*(7.2) = 4*(9.0)   ?    [cross-multiply]

          36.0  =  36.0   ? yes

 

What is the diagonal?

     W²+ H² = D²

    (9.0)² + (7.2)² = D²

       11.5 = D