Line segment AB is one unit long. If point C cuts AB so that AC = 0.618, what is the ratio of AC to CB? a. 1 c. 1.32 b. 1.618 d.

Question

seraphim [82]

4 years ago

12

Line segment AB is one unit long. If point C cuts AB so that AC = 0.618, what is the ratio of AC to CB? a. 1 c. 1.32 b. 1.618 d.

1.543

Mathematics

1 answer:

Alecsey [184] · Answer 1 · 2022-03-05T14:35:30+03:00

By the segment addition postulate,
AB = AC+CB
since C is somewhere between A and B

We know AC is 0.618 and AB = 1
CB = x for now

AB = AC+CB
1 = 0.618+x
1-0.618 = 0.618+x-0.618 ... subtract 0.618 from both sides
0.382 = x
x = 0.382

So CB is 0.382 units long

To find the ratio of AC to CB, divide the values
AC/CB = 0.618/0.382 = 1.618 (approximate to 3 decimal places)

Answer: Choice B) 1.618