Question

A "golden rectangle” is a rectangle where the ratio of the longer side to the shorter side is the "golden ratio.” These rectangles are said to be visually pleasing. An example of a "golden rectangle” has a length equal to x units and a width equal to x – 1 units. Its area is 1 square unit. What is the length of this golden rectangle?

Answer 1

The length of the golden rectangle is approximately 2.618 units.

Step-by-step explanation:

The length of the golden rectangle can be found by setting up a proportion using the given information. Let's represent the length of the rectangle as x units and the width as x - 1 units. The ratio of the length to the width is x / (x - 1). Since the rectangle is a golden rectangle, this ratio is equal to the golden ratio, which is approximately 1.618. Setting up the proportion, we have:

x / (x - 1) = 1.618

Now, to solve for x, we can cross multiply:

x = 1.618(x - 1)

x = 1.618x - 1.618

0.618x = 1.618

x = 2.618

Therefore, the length of the golden rectangle is approximately 2.618 units.

Answer 2

The answer is b. I just did the question and that is the answer