Question

The size of a TV set is described by the length of a diagonal of the screen. One TV is labeled as size 70cm. The screen is 40cm high.

What is the width of the screen?
Draw a diagram to illustrate your answer.

Answer 1

Width of screen =57.44 cm

Explanation:

Please refer to the attached image:

The TV screen is usually in the form of a rectangle.

The diagonal of the TV is termed as the screen size.

Size is given to be 70 cm

Height = 40 cm

As per the attached image:

BC = 40 cm

BD = 70 cm

Pythagoras theorem is given as:

`\text{Hypotenuse}^(2) = \text{Base}^(2) + \text{Height}^(2)`

Using pythagoras theorem in
`\triangle BDC`:

`BD^(2)= BC^(2)+ CD^(2)`

`70^(2)= 40^(2)+ CD^(2)\\\Rightarrow CD^(2) =4900 - 1600\\\Rightarrow CD^(2) =3300\\\Rightarrow CD =57.44 cm`

Hence, width of screen, CD =57.44 cm