SOLUTION: Trying to find the length of the 2 sides of a rectangle. Only have the length of the line dissecting the rectangle. Thought using the Pythagorean would be the way to go but got s

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Question 439895: Trying to find the length of the 2 sides of a rectangle. Only have the length of the line dissecting the rectangle. Thought using the Pythagorean would be the way to go but got stumped when using the ratios, as I don't have any of the side measurements.
Given:
C=21.5
Ratio of A:B = 16:9
Just a nudge in the right direction would be awesome. Thanks in advance!
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Trying to find the length of the 2 sides of a rectangle. Only have the length of the line dissecting the rectangle. Thought using the Pythagorean would be the way to go but got stumped when using the ratios, as I don't have any of the side measurements.
Given:
C=21.5
Ratio of A:B = 16:9
-----
71216:9 is the same as 16x:9x
------------------
Pythagoras:
(9x)^2+(16x)^2 = 21.5^2
-----
{81+256]x^2 = 462.25
x^2 = 1.3717
----
x = 1.1712...
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Cheers,
Stan H.
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Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
sounds like "wide screen" aspect ratio

use a "fudge factor" (proportionality constant) to find the lengths

(9k)^2 + (16k)^2 = 21.5^2