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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?

Respuesta :

apologiabiology
area=length times width


area=1=x times (x-1)

1=x(x-1)
1=x^2-x
0=x^2-x-1
using quadratic formula
for
0=ax^2+bx+c
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
for
0=1x^2-1x-1
a=1
b=-1
c=-1

[tex]x= \frac{-(-1)+/- \sqrt{(-1)^2-4(1)(-1)} }{2(1)} [/tex]
[tex]x= \frac{1+/- \sqrt{1+4} }{2} [/tex]
[tex]x= \frac{1+/- \sqrt{5} }{2} [/tex]

[tex]x= \frac{1+ \sqrt{5} }{2} [/tex] or [tex]x= \frac{1- \sqrt{5} }{2} [/tex]
the 2nd one will be negative so we reject that because we can't have negative lengths

so
[tex]x= \frac{1+ \sqrt{5} }{2} [/tex]
the length is [tex] \frac{1+ \sqrt{5} }{2} [/tex]
dhanyaj

Answer:

B because

Step-by-step explanation:

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?

and it is

1+ root 5 divided by 2

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