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valina [46]
4 years ago
15

Determine the unknown side length of the golden rectangle with the given side length. s = _____, l=9 a. 5.56 c. 4.94 b. 4.85 d.

5.26
Mathematics
1 answer:
andreyandreev [35.5K]4 years ago
5 0

The side lengths of the golden rectangle are in the proportion ⇒ 1 : golden number

golden number = \frac{1+\sqrt{5} }{2}

So, the ratio = 1 : \frac{1+\sqrt{5} }{2} = \frac{1}{\frac{1+\sqrt{5} }{2}} = \frac{2}{1+\sqrt{5}}

Since we have given side l = 9, we can use the proportion, to find the unknown lenght s.

∴ \frac{2}{1+\sqrt{5}} = \frac{s}{l}

∴ \frac{2}{1+\sqrt{5}} = \frac{s}{9}

Solve for s.

∴ s = 9 * \frac{2}{1+\sqrt{5}} = \frac{18}{1+\sqrt{5}}

using the calculator

∴ s ≈ 5.56

<u>So, the correct answer is option a. 5.56</u>

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