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

Answer:

Width of screen =57.44 cm

Step-by-step 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