SOLUTION: I have a golden rectangle with a diagonal of 10 cm. What is it width value [x]? No length value is given. How do I solve for x?

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Question 711640: I have a golden rectangle with a diagonal of 10 cm. What is it width value [x]? No length value is given.
How do I solve for x?

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
In a golden rectangle, length and width are related by the ratio
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The diagonal splits the rectangle into 2 congruent right triangles.
The legs lengths are and ,
and the hypotenuse is the diagonal so its length is .
The Pythagorean theorem says
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Multiplying both sides of the equal sign times 4 we get
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At this point, we can calculate an approximate value for as a decimal number,
and then find its square root for a good approximation of .
If we want an exact value, all we can get is a more or less complicated expression with square roots:
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