One of the most studied and interesting visual and numerical concepts in algebra is the Golden...

 

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One of the most studied and interesting visual and numerical concepts in algebra is the Golden Ratio. Ancient Greeks thought (and many people still do) that a rectangle was most aesthetically pleasing to the eye if the ratio of its length to its width is the Golden Ratio (about 1.618). In fact, the Parthenon, built by Greeks in the fifth century B.C., utilizes the Golden Ratio. A rectangle is "golden" if its length, L, and width, w, satisfy the equation W w L-w L 1 L-1 a. 18 pts] By letting w=1 unit in the equation above, we get the equation 1 positive value of L (which is the algebraic expression for the golden ratio). Solve this equation for the b. [6 pts] Suppose that an architect is constructing a building with a rectangular front that is to be 60 feet high. About how long should the front be if she wants the appearance of a golden rectangle? (Assume w=60 ft and that you are looking for L.) Round to 2 decimal places. One of the most studied and interesting visual and numerical concepts in algebra is the Golden Ratio. Ancient Greeks thought (and many people still do) that a rectangle was most aesthetically pleasing to the eye if the ratio of its length to its width is the Golden Ratio (about 1.618). In fact, the Parthenon, built by Greeks in the fifth century B.C., utilizes the Golden Ratio. A rectangle is "golden" if its length, L, and width, w, satisfy the equation W w L-w L 1 L-1 a. 18 pts] By letting w=1 unit in the equation above, we get the equation 1 positive value of L (which is the algebraic expression for the golden ratio). Solve this equation for the b. [6 pts] Suppose that an architect is constructing a building with a rectangular front that is to be 60 feet high. About how long should the front be if she wants the appearance of a golden rectangle? (Assume w=60 ft and that you are looking for L.) Round to 2 decimal places.

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Golden rectangles dimension follow the equation L Now ... View the full answer