Jon went to his local electronics store and purchased an HDTV whose screen measured 64 inches diagonally, and whose aspect ratio was 16 to 9. Find the width and height of the screen. Round to the nearest tenth.
A)width: 57.9 in; height: 34.0 in
B)width: 54.5 in; height: 32.9 in
C)width: 55.8 in; height: 31.4 in
D)width: 55.0 in; height: 30.2 in
E)width: 54.0 in; height: 32.8 in

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can set up the equation:
(16x)^2 + (9x)^2 = 64^2
256x^2 + 81x^2 = 4096
337x^2 = 4096
x^2 = 12.15
x = 3.49 (rounded to nearest hundredth)
Therefore, the width is 16x = 55.8 (rounded to nearest tenth)
And the height is 9x = 31.4 (rounded to nearest tenth)
Thus, the best choice is C.

Jon Went to His Local Electronics Store and Purchased an HDTV