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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?

Respuesta :

DeanR

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

[tex]p = 4x + 3x + 4x + 3x = 14x[/tex]

The diagonal is given by the Pythagorean Theorem

[tex]20^2 = (4x)^2 + (3x)^2 [/tex]

[tex]4^2 (5^2)= (4^2 + 3^2) x^2[/tex]

[tex]4^2 (5^2)= (5^2) x^2[/tex]

[tex] x^2 = 4^2[/tex]

We're only interested in positive lengths,

[tex]x = 4[/tex]

[tex]p = 14(4) = 56[/tex]

Answer: 56


jackdurham64

Answer:

56

Step-by-step 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.

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