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Golden rectangle in a triangle

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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.

Jan 3, 2021

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The longer side of a rectangle should be on the side BC.

Jan 3, 2021
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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

Jan 3, 2021