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The diagonal of the TV is 140cm. The ratio of the height to the length of the screen is 9:16. Can the TV fit lengthwise between two shelves that are 120cm apart?

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Answer to a math question The diagonal of the TV is 140cm. The ratio of the height to the length of the screen is 9:16. Can the TV fit lengthwise between two shelves that are 120cm apart?

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Hank
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101 Answers
1. Neka je visina televizora h i duljina televizora l . Zbog omjera visine i duljine \frac{h}{l} = \frac{9}{16} , imamo h = \frac{9}{16}l .

2. Primjenom Pitagorinog poučka na pravokutni trokut kojeg sačinjavaju visina, duljina i dijagonala televizora, imamo jednadžbu:

h^2 + l^2 = 140^2

3. Zamjenjujući h s \frac{9}{16}l u jednadžbi:

\left( \frac{9}{16}l \right)^2 + l^2 = 140^2

4. Pojednostavljujući i rješavajući za l :

\frac{81}{256}l^2 + l^2 = 19600

\frac{337}{256}l^2 = 19600

l^2 = 19600 \cdot \frac{256}{337}

l=\sqrt{14867.96}\approx122.02\text{ cm}

5. Provjerom, duljina l\approx122.02\text{ cm}
, premašuje razmak između polica od 120 cm, pa televizor ne može stati.

Since 122.1 cm > 120 cm, the TV cannot fit between the two shelves.

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