What is the width of television screen?

Question

A televisión is measured by its diagonal length across the screen. If the screen measures 50 inches and the height is 40 inches, what is the width of television screen?

Answer 1

diagonal = d; width = w; height = h

width, height and diagonal of the tv make a right triangle.

d^2 = w^2 + h^2 by Pythagoras theorem

50^2 = w^2 + 40^2

w^2 = 50^2 - 40^2 = 2500 - 1600 = 900

w = sqrt(900) = 30

Hence width of the TV screen is 30 inches.

Remember these 2 special right triangles:

1. right triangle with perpendicular sides 3 and 4, has a hypotenuse of 5. So 3,4,5 triangle rule.
2. If you scale this by 10 (each side is 10 times longer), you will get 30,40,50
3. and scale it by 2, your right triangle has sides 6,8,10 (10 is hypotenuse)
4. Similarly right triangle with sides 5,12,13 (13 is hypotenuse).

You will come across these two special cases in many problems.

Answer 2

30 inches wide

it's a 3-4-5 right triangle inflated by a factor of 10

W^2 = 50^2 - 40^2 = 2500 - 1600 = 900

W =sqr900 = 30 inches wide