Alg 1

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A golden rectangle is 32 cm long. The ratio of length to width is (1 + sq rt 5)/2. What is the width of the rectangle in simplest radical form?

Please solve and explain. Thanks.

  • Alg 1 -

    L = Length

    W = Width


    L / W = ( 1 + sqrt 5 ) / 2

    Reciprocally :

    W / L = 1 / [ ( 1 + sqrt 5 ) / 2 ]

    W / L = 2 / [ ( 1 + sqrt 5 ) ] Multiply both sides by L

    W = 2 L / 2 / [ ( 1 + sqrt 5 ) ]

    W = 2 * 32 / [ ( 1 + sqrt 5 ) ]

    W = 64 / [ ( 1 + sqrt 5 ) ]

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