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# Many television screens are rectangles that are measured by the length

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
Many television screens are rectangles that are measured by the length  [#permalink]

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20 Mar 2019, 02:22
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Difficulty:

35% (medium)

Question Stats:

80% (02:21) correct 20% (02:47) wrong based on 25 sessions

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Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following?

(A) 20
(B) 20.5
(C) 21
(D) 21.5
(E) 22

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Re: Many television screens are rectangles that are measured by the length  [#permalink]

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20 Mar 2019, 02:40
Bunuel wrote:
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following?

(A) 20
(B) 20.5
(C) 21
(D) 21.5
(E) 22

For length and height ration 4:3 the diagonal will have length $$= √(4^2+3^2) = 5$$

now 5x = 27
i.e. x = 27/5

Length = 4x = 4*(27/5) = 21.6 inches

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Re: Many television screens are rectangles that are measured by the length  [#permalink]

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20 Mar 2019, 06:45
Bunuel wrote:
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following?

(A) 20
(B) 20.5
(C) 21
(D) 21.5
(E) 22

the diagonal of the TV = √4^2+3^2 = 5
so
27 inch tv would have ; 5x= 27; x=27/5 diagonal ; 4x
or say 4*27/ 5 = 21.6
IMO D
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Re: Many television screens are rectangles that are measured by the length  [#permalink]

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22 Mar 2019, 09:12
Bunuel wrote:
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following?

(A) 20
(B) 20.5
(C) 21
(D) 21.5
(E) 22

We can let the horizontal length of the screen = 4x and the height of the screen = 3x. By the Pythagorean theorem, we have:

(4x)^2 + (3x)^2 = 27^2

16x^2 + 9x^2 = 27^2

25x^2 = 27^2

x^2 = 27^2/25

x = √(27^2/25) = 27/5 = 5.4

Therefore, the horizontal length of the screen is 4(5.4) = 21.6 inches, which is closest to 21.5.

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Re: Many television screens are rectangles that are measured by the length   [#permalink] 22 Mar 2019, 09:12
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