Higher Math....TV Screen Size Formula?

Question

I want to prove that a 46" 4:3 TV has more screen area in square inches than a 46" 16:9 TV. I know that you would figure the area of the two triangles that make up the screen (A=1/2B x H)x 2, but I don't know the formula to find the lenghth of the sides. Tried SOHCAHTOA, couldn't remember how to do it.

Answer 1

Well, try logic. If you have the same dimension, then remember that you always get the most area out of a square rather than a rectangle.



As for mathematically, think of it this way. 4:3 means that the height is 3/4 of the length. And as such, 16:9 means that the length is almost twice the distance of the height. So if you have two 46" tvs, with different heights and widths, you need to find some equations to help you out.



4:3 television:

In a 3-4 right triangle, the hypotenuse is always 5. so now you have some ratios to work with.

46/5 = x/4 & 46/5 = y/3

x = 36.8 & y = 27.6

So your area equals 1015.68 sq in.



16:9 television:

sqrt(16^2 + 9^2) = about 18.36.

Using same idea as before....

46/18.36 = x/16 & 46/18.36 = y/9

x = 40.09 & y = 22.55

So your area equals 904.03 sq in.

Answer 2

Here's how I solved it. I don't know if it is the correct formula, but it does show the 4:3 has more screen size.



The 46 inch diagonal is the hypotenuse of a right triangle whose other sides are "H" and "W". In both cases the area is H*W and H^2 + W^2 = (46)^2, and the task is to see which screen size has the larger area.



the 4:3 screen



4W = 3H

W = (3/4)H

(3/4H)^2 + H^2 = (46)^2

(9/16)H^2 + (16/16)H^2 = 2116

H^2 = 2116(16/25)

H = 54.17

W = 40.62

A = 2200.8



////////////////////////////



the 16:9 screen

16W = 9H

W=(9/16)H

(9/16H)^2 + H^2 = (46)^2

(81/256)H^2 + (256/256)H^2 = 2116

H^2 = 2116(256/337)

H = 40.08

W = 22.55

A = 903.80



The 3:4 screen is thus 243% larger than the 9:16 screen

Answer 3

In your 4:3 TV the Hypotenuse will be 46"

In your 16:9 TV the Hypotenuse will be 46"





In first case the Ratio 3:4:5 is x:y:46



In any 3 4 5 case

the Cos = 0.8[4/5]{CAH}

the Sin = 1.25[5/4]{SOH}

the Tan = 1.33[4/3]{TOA}





in 16:9 if we have multiplied 4 x 4 & 3 x 3 Then Hyptoneuse = Sqr rt of 46

Answer 4

Mathtv

Answer 5

Mathtv.com