SOLUTION: Television sets are measured diagonally from corner. HDTVs are designed so that the proportion of width to height is 16 to 9. Use this information to find the actual dimensions (wi

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Question 459662: Television sets are measured diagonally from corner. HDTVs are designed so that the proportion of width to height is 16 to 9. Use this information to find the actual dimensions (width and height) of a 46 inch HDTV
Answer by nerdybill(7384) About Me  (Show Source):
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Television sets are measured diagonally from corner. HDTVs are designed so that the proportion of width to height is 16 to 9. Use this information to find the actual dimensions (width and height) of a 46 inch HDTV
.
Let x = width
and y = length
.
because of the 16 to 9 ratio we have:
16/9 = y/x
cross multiplying
16x = 9y
16x/9 = y
.
applying Pythagorean theorem:
x^2 + (16x/9)^2 = 46^2
x^2 + 256x^2/81 = 2116
81x^2 + 256x^2 = 171396
x^2(81 + 256) = 171396
x^2(337) = 171396
x^2 = 171396/337
x^2 = 508.593
x = 22.55 inches (width)
.
Length:
16x/9 = 16(22.55)/9 = 360.8/9 = 40.09 inches