SOLUTION: what would be the length of the long side of a golden rectangle if the short side is 24 inches

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Question 418955: what would be the length of the long side of a golden rectangle if the short side is 24 inches
Found 2 solutions by josmiceli, rfer:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
call the short side y and the long side x
For a golden rectangle:
y%2Fx+=+x%2F%28y+%2B+x%29
---------
given:
y+=+24 in
+24%2Fx+=+x%2F%2824+%2B+x%29+
+24%2A%2824+%2B+x%29+=+x%5E2+
+576+%2B+24x+=+x%5E2+
x%5E2+-+24x+-+576+=+0
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-24
c+=+-576
x+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2+-+4%2A1%2A%28-576%29+%29%29%2F%282%2A1%29+
x+=+%28+24+%2B-+sqrt%28+576++%2B+2304+%29%29%2F+2+
x+=+%28+24+%2B-+sqrt%28+2880+%29%29%2F+2+
x+=+%28+24+%2B-+24%2Asqrt%28+5+%29%29%2F+2+
x+=+24%2A%281+%2B+sqrt%285%29%29+%2F+2+
x+=+12%2A%281+%2B+sqrt%285%29%29+

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
1:1.618
24*1.618=38.8 in