Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are 36 inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows? a. 32 inchesb. 42 inchesc. 55 inchesd. 60 inches

Answer: a. 32 inches

Step-by-step explanation:

Hi, to solve this problem we have to apply Pythagoras's theorem.

a² + b² = c²

Where c is the longest side of the triangle (formed by the height, width and diagonal of the TV), and a & b are the other two sides

If we try with option a), diagonal is 32 inches, tall is x and width is 2x.

Mathematically speaking:

32 ² = x² + 2x²

1024 = 3 x²

1024/3 = x²

√341.34=x

18.4752=x

We obtain that for option a) 32 inches, the height of the TV is 18.4752 and its width is approximately 36.9 (2x = 2 (18.47) = 36.9)

36.9≅36 (distance between windows)

Option a is the lowest value, the other options will give greater values of width.

So, the correct option is a. 32 inches.