Lesson 16When Is the Same Size Not the Same Size?

Learning Goal

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

Learning Targets

I can apply what I have learned about the Pythagorean Theorem to solve a more complicated problem.
I can decide what information I need to know to be able to solve a real-world problem using the Pythagorean Theorem.

Warm Up: Three Figures

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

Three rectangles of differing sizes, all with a diagonal line drawn from corner to corner.

Activity 1: A 4:3 Rectangle

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

Problem 1

What does it mean that the aspect ratio is $4 : 3$ ? Mark up the diagram to show what that means.

Problem 2

If the shorter side of the rectangle measures 15 inches:

What is the length of the longer side?
What is the length of the rectangle’s diagonal?

Problem 3

If the diagonal of the $4 : 3$ rectangle measures 10 inches, how long are its sides?

Problem 4

If the diagonal of the $4 : 3$ rectangle measures 6 inches, how long are its sides?

Activity 2: 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?