Question

The aspect ratio of a TV screen is the ratio of the horizontal length to the vertical height. If the TV has a diagonal of 100 cm and the aspect ratio is 4:3, then find the horizontal length and the vertical height of the TV screen.

Answer 1

horizontal length=80, vertical length=60

Explanation:

a^2 + b^2 = c^2

the tv is a 3:4:5 right triangle

the ratio is then changed from

3:4:5

to

60:80:100

because 100/5 = 20

so you multiply the original ratio by 20

(because the length of 100 that we are given is the hypotenuse of the triangle(diagonal of the tv))

Therefore,

the horizontal length is 80

the vertical lengt is 60

Answer 2

The horizontal length is 80 cm, and the vertical height is 60 cm.

Explanation:

The aspect ratio is the ratio of the horizontal length to the vertical height.

We have a rectangle with sides 4 and 3. We can find the length of the diagonal.

We can use the Pythagorean theorem to find the length of the diagonal.

a^2 + b^2 = c^2

3^2 + 4^2 = c^2

9 + 16 = c^2

c^2 = 25

c = 5

The diagonal is 5 in the ratio.

The ratio of the horizontal length to the vertical height to the diagonal is

4:3:5

We multiply all the numbers in the ratio by the same unknown, x.

A ratio of 4:3:5 is the same as a ratio of 4x:3x:5x.

We are told that the diagonal is 100 cm, so we have

4x : 3x : 100,

but we already had a ratio of

4x : 3x : 5x, so

5x = 100, and we can find x.

5x = 100

Divide both sides by 5.

x = 20

Since x = 20, then the horizontal length 4x = 4(20) = 80,

and the vertical height 3x = 3(20) = 60

Answer: The horizontal length is 80 cm, and the vertical height is 60 cm.