Question

Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)

Answer 1

The scale factor is equal to 1/2

The dimensions of each channel when splits the screen is 46 in x 38 in

Explanation:

we know that

The dimensions of the new television is 92 in x 76 in

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

A1 -----> the area of the new television

A2 ----> the area of each channel when splits the screen

z-----> the scale factor

`z^(2) =(A2)/(A1)`

we have that

The area of the new television is 4 times the area of each channel

`A1=4A2`

`(A2/A1)=1/4`

`z^(2) =(1)/(4)`

`z=(1)/(2)` -----> the scale factor

so

When splits the screen, the dimension of each channel is equal to

92/2 in x 76/2 in

so

46 in x 38 in

Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides

Verify the value of the scale factor

92/46=1/2

or

76/38=1/2