Question

1) For her birthday, your grandmother wants you to replace her old, tube TV with a new, widescreen TV. Her current TV measures 42" and she would like her new TV to measure the same size. What are the dimensions of the new TV if the aspect ratio is 16:97​

Answer 1

Dimensions are 36.608 inches by 20.592 inches

Both values are approximate, rounded to 3 decimal places.

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Step-by-step explanation:

I'm assuming you meant to say 16:9 instead of 16:97

The ratio 16:9 means that the horizontal width is 16x units and the height is 9x units. They form the ratio 16x:9x which reduces to 16:9

She wants the tv to be the same size as her old one, so the new tv will also have a diagonal of 42 inches (tv sizes are measured by the length of the diagonal).

Through the pythagorean theorem, we can say

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 approximately

x = sqrt(5.23442136498517)

x = 2.28788578495194

x = 2.288

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This means the dimensions would be

width = 16x = 16*2.288 = 36.608 inches

height = 9x = 9*2.288 = 20.592 inches

both are approximate