SOLUTION: What is the area of a golden rectangle of height 2". I get how to draw it out but I am struggling with the formulas?

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Question 432524: What is the area of a golden rectangle of height 2". I get how to draw it out but I am struggling with the formulas?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the length +x+
The formula is:
+2%2Fx+=+x%2F%28x%2B2%29+
Multiply both sides by +x%2A%28x%2B2%29+
+2%2A%28x%2B2%29+=+x%5E2+
+2x+%2B+4+=+x%5E2+
+x%5E2+-+2x+-+4+=+0+
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=+1
b+=+-2
c+=+-4
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+
x+=+%28+2+%2B-+sqrt%28+4+%2B+16+%29%29%2F2+
+x+=+%282+%2B-+sqrt%28+4%2A5%29%29%2F2+
+x+=+2%2F2+%2B+2%2Asqrt%285%29%2F2+
+x=+1+%2B+sqrt%285%29+
The other root is negative, so it can't be used
The area is A+=+x%2A2
+A+=+2%2A%281+%2B+sqrt%285%29%29
+A+=+2+%2B+2%2Asqrt%285%29+ in.