# Question Video: Understanding Proportions

The ratio between Noah’s and Benjamin’s heights is 3 : 4. If Benjamin is 144 cm tall, how tall is Noah?

01:50

### Video Transcript

The ratio between Noah’s and Benjamin’s heights is three to four. If Benjamin is 144 centimeters tall, how tall is Noah?

We are told in the question that the ratio of heights is three to four. As Noah was mentioned first, he will correspond to the first number. Benjamin will therefore correspond to the second number, in this case four. We are also told that Benjamin is 144 centimeters tall. As his height was four parts of the ratio, we can divide 144 by four to calculate one part. 14 divided by four is equal to three remainder two. 24 divided by four is equal to six. Therefore, 144 divided by four is 36. One part of the ratio is therefore equal to 36 centimeters.

In order to calculate Noah’s height, we now need to multiply 36 by three. 30 multiplied by three is equal to 90, and six multiplied by three is equal to 18. This means that 36 multiplied by three is equal to 108. The ratio three to four is equivalent to 108 to 144, as we’ve multiplied both sides by 36. We can therefore conclude that Noah is 108 centimeters tall.