Question

The ratio of corresponding side lengths of two similar MP3 players is 4:3. The area of the larger MP3 player is 8 square inches. What is the area of the smaller MP3 player?

Answer 1

The area of smaller mp3 player is 4.5 square inches

Solution:

Given that ratio of corresponding side lengths of two similar MP3 players is 4:3

The area of the larger MP3 player is 8 square inches

To find: area of the smaller MP3 player

If two MP3 players are similar, then their corresponding sides are proportional.

To find the area ratios, raise the side length ratio to the second power

`\frac{\text {area of larger mp3}}{\text {area of smaller mp3}}=\left((4)/(3)\right)^(2)`

From given information,

area of larger mp3 = 8 square inches

Let the area of smaller mp3 = x

So the above ratio becomes,

`(8)/(x)=\left((4)/(3)\right)^(2)\\\\(8)/(x) = (16)/(9)\\\\16x = 9 * 8\\\\16x = 72\\\\x = 4.5`

Thus the area of smaller mp3 player is 4.5 square inches