Lesson 16

When Is the Same Size Not the Same Size?

  • Let’s figure out how aspect ratio affects screen area.

16.1: Three Figures

How are these shapes the same? How are they different?

Three quadrilaterals.

 

16.2: A $4:3$ Rectangle

A typical aspect ratio for photos is \(4:3\). Here’s a rectangle with a \(4:3\) aspect ratio. 

Rectangle. 
  1. What does it mean that the aspect ratio is \(4:3\)? Mark up the diagram to show what that means.
  2. If the shorter side of the rectangle measures 15 inches:
    1. What is the length of the longer side?
    2. What is the length of the rectangle’s diagonal?
  3. If the diagonal of the \(4:3\) rectangle measures 10 inches, how long are its sides?
  4. If the diagonal of the \(4:3\) rectangle measures 6 inches, how long are its sides?

16.3: The Screen Is the Same Size . . . Or Is It?

Before 2017, a smart phone manufacturer’s phones had a diagonal length of 5.8 inches and an aspect ratio of \(16:9\). In 2017, they released a new phone that also had a 5.8-inch diagonal length, but an aspect ratio of \(18.5:9\). Some customers complained that the new phones had a smaller screen. Were they correct? If so, how much smaller was the new screen compared to the old screen?

Summary