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?

length of golden rectangle = 1.618

Step-by-step explanation:

It is given that the length (L) of golden rectangle is x

And width (W) of rectangle is x-1

so we have

L = x

W= x-1

Now we have area of rectangle given by

Area = L × W

Area = x(x-1)                             ( we plug L= x and W= x-1)

It is given that area of rectangle is 1 square unit.

So we have

      ( distribute x and remove parenthesis )

   ( subtract 1 from both sides )

Now to solve for x we need to use the quadratic formula

For quadratic equation

The quadratic formula is given by

Here we have a= 1 , b=-1 c=-1 , so we have

 or  

or x=-0.618

We can not have length negative

hence

length of golden rectangle = 1.618

step-by-step explanation:

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