SOLUTION: Solving Quadratic Equations Using Square Root/Factoring The aspect ratio of a TV screen is the ratio of the screen’s width to its height. For HDTVs, the aspect ratio is 16:9. Wh

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solving Quadratic Equations Using Square Root/Factoring The aspect ratio of a TV screen is the ratio of the screen’s width to its height. For HDTVs, the aspect ratio is 16:9. Wh      Log On


   

Question 903826: Solving Quadratic Equations Using Square Root/Factoring
The aspect ratio of a TV screen is the ratio of the screen’s width to its height. For HDTVs, the aspect ratio is 16:9. What is the width and height of a 42 inch screen TV? (42 inches refers to the length of the screen’s diagonal.) HINT: Use the Pythagorean Theorem. Round your answers to the nearest hundredth.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
16:9 means
width = 16x
height = 9x
for some number x

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a^2 + b^2 = c^2

(16x)^2 + (9x)^2 = 42^2

256x^2 + 81x^2 = 1764

337x^2 = 1764

x^2 = 1764/337

x^2 = 5.23442136498517 (this is approximate)

x = sqrt(5.23442136498517) (this is approximate)

x = 2.28788578495194 (this is approximate)

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Width: 16x = 16*2.28788578495194 = 36.606172559231

Height: 9x = 9*2.28788578495194 = 20.5909720645674

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Summary:


Width: 36.606 inches

Height: 20.591 inches

Answers are approximate. I rounded the final values to 3 decimal places