Triangle ABC has sides AB = 6, AC = 8, and BC = 12. The golden rectangle is inscribed in a triangle so that two of its vertices are on side BC and the other two vertices are on sides AB and AC. Find the area of a rectangle.
+1641 Triangle ABC has sides AB = 6, AC = 8, and BC = 12. The golden rectangle is inscribed in a triangle so that two of its vertices are on side BC and the other two vertices are on sides AB and AC. Find the area of a rectangle. The longer side of a rectangle should be on the side BC.
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A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1 : (1 + √5) / 2
If the short side of a rectangle is x then the longer side is x * [(1 + √5) / 2]
Find angles B and C using the law of cosines.
Use this formula to calculate the sides of a rectangle:
x / tan∠B + x * [(1 + √5) / 2] + x / tan∠C = 12
