Question

A rectangular flat-screen computer monitor has a diagonal that measures 20 inches. the ratio of the length of the screen to the width of the screen is 4 to 3. what is the perimeter of the screen, in inches?

Answer 1

56

Explanation:

Using the diagonal measurement we can see that there is a triangle in the rectangle. 4:3 ratio means that the triangle has a 3-4-5 ratio or in measurements: 12-16-20. Each measurement has a difference of four.

Add the length (16) and width (12) twice to get 56 as the perimeter.

Answer 2

Let's call the length 4x and the width 3x. Then the perimeter is

`p = 4x + 3x + 4x + 3x = 14x`

The diagonal is given by the Pythagorean Theorem

`20^2 = (4x)^2 + (3x)^2`

`4^2 (5^2)= (4^2 + 3^2) x^2`

`4^2 (5^2)= (5^2) x^2`

`x^2 = 4^2`

We're only interested in positive lengths,

`x = 4`

`p = 14(4) = 56`

Answer: 56