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01 Jan 2025, 09:18
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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100% (03:51) wrong based on 1 sessions
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The “aspect ratio” of a rectangular TV screen is the ratio of its width to its height.
Quantity A
The area of a rectangular TV screen with an aspect ratio of 4:3 and a diagonal of 25"
Quantity B
The area of a rectangular TV screen with an aspect ratio of 16:9 and a diagonal of 25"
Quantity A
The area of a rectangular TV screen with an aspect ratio of 4:3 and a diagonal of 25"
Quantity B
The area of a rectangular TV screen with an aspect ratio of 16:9 and a diagonal of 25"
04 Jan 2025, 13:04
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OE
For the TV in Quantity A, the aspect ratio of 4:3 means the width is 4x and the height is 3x, where x is some unknown multiplier. By Pythagorean theorem, the diagonal is:
\(\sqrt{a^2+b^2} = \sqrt{(4x)^2+(3x)^2} = \sqrt{16x^2+9x^2}=\sqrt{25x^2}=5x\)
You know that the diagonal is 25 inches, so x is 5. The width of the TV is (4)(5), which is 20, and the height is (3)(5), which is 15. Thus, the area is wh= (20)(15), which equals 300.
For the TV in Quantity B, the aspect ratio of 16:9 means the width is 16y and the height is 9y, where y is some unknown multiplier. By Pythagorean theorem, the diagonal is:
\(\sqrt{a^2+b^2} = \sqrt{(16y)^2+(9y)^2} = \sqrt{256y^2+81y^2}\)~ 18.3576y (use calculator). You know that the diagonal is 25 inches, so
\(y=\frac{25}{18.3576}~1.3618.\) The width of the TV is approximately (16)(1.3618), which is 21.7888, and the height is approximately (9) (1.3618), which is 12.2562.
Thus, the area is (width)(height) = (21.7888)(12.2562), which equals 267.05.
Thus, Quantity A is greater.
For the TV in Quantity A, the aspect ratio of 4:3 means the width is 4x and the height is 3x, where x is some unknown multiplier. By Pythagorean theorem, the diagonal is:
\(\sqrt{a^2+b^2} = \sqrt{(4x)^2+(3x)^2} = \sqrt{16x^2+9x^2}=\sqrt{25x^2}=5x\)
You know that the diagonal is 25 inches, so x is 5. The width of the TV is (4)(5), which is 20, and the height is (3)(5), which is 15. Thus, the area is wh= (20)(15), which equals 300.
For the TV in Quantity B, the aspect ratio of 16:9 means the width is 16y and the height is 9y, where y is some unknown multiplier. By Pythagorean theorem, the diagonal is:
\(\sqrt{a^2+b^2} = \sqrt{(16y)^2+(9y)^2} = \sqrt{256y^2+81y^2}\)~ 18.3576y (use calculator). You know that the diagonal is 25 inches, so
\(y=\frac{25}{18.3576}~1.3618.\) The width of the TV is approximately (16)(1.3618), which is 21.7888, and the height is approximately (9) (1.3618), which is 12.2562.
Thus, the area is (width)(height) = (21.7888)(12.2562), which equals 267.05.
Thus, Quantity A is greater.
