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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?

User Zack Tarr
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2 Answers

1 vote

Answer:

B because

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

User Holloway
by
7.3k points
3 votes
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

x= (-b+/- √(b^2-4ac) )/(2a)
for
0=1x^2-1x-1
a=1
b=-1
c=-1


x= (-(-1)+/- √((-1)^2-4(1)(-1)) )/(2(1))

x= (1+/- √(1+4) )/(2)

x= (1+/- √(5) )/(2)


x= (1+ √(5) )/(2) or
x= (1- √(5) )/(2)
the 2nd one will be negative so we reject that because we can't have negative lengths

so

x= (1+ √(5) )/(2)
the length is
(1+ √(5) )/(2)
User Ilya Rezvov
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7.5k points