Sam and Pete both have 55 inch TVS. Sam's tv has a 4:3 aspect ratio and Pete has a 16:9. How would you determine who actually has the larger tv screen? Find

Let N be the shorter side of Sam's TV screen

Then the longer side will be (4N/3)

Then, by the Pythagorean Theorem, we can solve this equation for N

N^2 + (4N/3)^2 =  55^2  

And    N  = 33  in     And the longer side  = (4 *33 / 3)  =  44 in

So.......the dimensions of Sam's set =  33 in x 44 in

Let M be the shorter side of Pete's TV screen

Then, the longer side will be (16M/9)

And, using the same logic we have

M^2 + (16M/9)^2   = 55^2     and  M≈26.964 in    And the longer side  ≈  (16 * 26.964 / 9) ≈ 47.936 in

So.....the dimensions of Pete's set = 26.964 in  x 47.936 in

The area of Sam's screen  = (33 * 44)in^2 =  1452 in ^2

And the area of Pete's screen  = ( 26.964 * 47.936)  in^2 =  1292.55 in^2

So....in terms of area.........Sam has the bigger screen