SOLUTION: An artist wants her painting to be in the shape of a golden rectangle. If the length of the painting is 36 inches, then what should be the width?

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Question 175758: An artist wants her painting to be in the shape of a golden rectangle. If the length of the painting is 36 inches, then what should be the width?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If the width (shorter length) of a golden rectangle is 1, then the length is %281+%2B+sqrt%285%29%29%2F2. So for this situation, if the width is x and 36 is the length,

%28x+%281+%2B+sqrt%285%29%29%29%2F2+=+36

Solve for x:

x+=+%2836+%2A+2%29%2F%281+%2B+sqrt%285%29%29+=+72%2F%281+%2B+sqrt%285%29%29

Now rationalize the denominator using the conjugate of %281+%2B+sqrt%285%29%29, namely 1+-+sqrt%285%29%29, so:



That's the exact answer. If you need a numerical approximation, use your calculator. However, round your answer to the nearest inch because you should never, unless specifically instructed otherwise, express an answer to a calculation involving measurements to a greater precision than the least precise given measurement. In this case, the length was expressed to the inch, so your answer must be to the nearest inch.