Question

A square image has a side length of 7 cm on a computer monitor. It is projected on a screen using an LCD projector. When projected, 1 cm of the image on the monitor represents 8 cm on the screen. Find the perimeter of the square in the projection.

answers are 392, 224, 448

Answer 1

224cm

Explanation:

The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm

square on the screen.

The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.

The side length of the square in the projection is the product of the side length of the preimage and the scale factor.

h=7(8)

cm

Simplify.

h=56

cm

The perimeter of the square is

P=4(56)

cm

Simplify.

P=224

cm

Therefore, the perimeter of the square in the projection is 224

cm.

Answer 2

The perimeter of the square in the projection is
`224\ cm`

Explanation:

we know that

1 cm of the image on the monitor represents 8 cm on the screen

so

using proportion

Find out how much represent on the screen 7 cm on a computer monitor

Let

x ----> the length side of the square image on the screen

`(1)/(8)(monitor)/(screen) =(7)/(x)(monitor)/(screen) \\ \\x=8*7\\ \\x=56\ cm`

Find the perimeter of the image on the screen

the perimeter of a square is equal to

`P=4b`

`b=56\ cm`

substitute

`P=4(56)=224\ cm`