 Televisions (indeed, all screens) are measured diagonally. When Best Buy lists a TV as having a 42-inch screen, it means 42 inches on the diagonal. Yet even though this is advertised as the screen's size, the diagonal only tells us part of the story about how much screen there is.

In this lesson, students use the Pythagorean Theorem along with some proportional reasoning to investigate the relationship between the diagonal length, aspect ratio, and screen area of a TV.

### Students will

• Understand the meaning of aspect ratio and use rectangle side ratios to solve problems
• Use the Pythagorean Theorem to find the length of an hypotenuse
• Use aspect ratio and the Pythagorean Theorem together to solve multi-step problems
• Understand that area does not grow in proportion to diagonal length

### Before you begin

Students should already be reasonably comfortable using the Pythagorean Theorem to find unknown side lengths in a right triangle, and understand that a diagonal partitions a rectangle into two congruent right triangles. This lesson also relies on students being able to apply an understanding of ratio and proportional reasoning. Finally, although alternate solutions exist, the solutions provided require squaring a monomial, i.e. (9u)2 = 81u2.

#### Shoutouts

Sharp USA, Apple, Phil Schiller, c|net, 60 Minutes, Dallas Cowboys, Jerry Jones, MacLife