SOLUTION: an american flag has the shape of the golden rectangle. the flags longer side is 5 feet less than twice the length of its shorter side. find the dimensions of the flag, rounded to

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Question 1151231: an american flag has the shape of the golden rectangle. the flags longer side is 5 feet less than twice the length of its shorter side. find the dimensions of the flag, rounded to the nearest foot.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Make 2 lengths add up to +1+ and
be in golden ratio to each other.
+x+%2F+%28+1+-+x+%29+=+%28+1+-+x+%29+%2F+1+
+x+=+%28+1+-+x+%29%5E2+
+x+=+1+-+2x+%2B+x%5E2+
+x%5E2+-+3x+%2B+1+=+0+
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+x+=+%28+-%28-3%29+%2B-+sqrt%28+9+-+4%2A1%2A1+%29%29+%2F+%28+2%2A1%29+
+x+=+%28+3+-+sqrt%28+5+%29%29+%2F+2+
and
+1+-+x+=+2%2F2+-+%28+3+-+sqrt%285%29+%29+%2F+2+
+1+-+x+=+%28+2+-+3+%2B+sqrt%285%29+%29+%2F+2+
+1+-+x+=+%28+-1+%2B+sqrt%285%29+%29+%2F+2+
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Let the length of the shorter side = +y+
+2y+-+5+ = length of the longer side
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+y+%2F+%28+2y+-+5+%29+=+%28+3+-+2.2361+%29+%2F+%28+-1+%2B+2.2361+%29+
+y+%2F+%28+2y+-+5+%29+=+.7639+%2F+1.2361+
+y+%2F+%28+2y+-+5+%29+=+.618+
+y+=+.618%2A%28+2y+-+5+%29+
+y+=+1.236y+-+3.09+
+.236y+=+3.09+
+y+=+13.093+
and
+2y+-+5+=+2%2A13.093+-+5+
+2y+-+5+=+26.186+-+5+
+2y+-+5+=+21.186+
To the nearest foot, the dimensions are
13 x 21
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check the math & get 2nd opinion if needed