Question

If AD = 2/3AB , what is the ratio of the length of (arc) BC to the length of (arc) DE ?

1/6

1/4

2/3

3/2

3/4

Answer 1

@pooja195

Answer 2

I think it's c

Answer 3

@Hero

Answer 4

Please note that, we have, by definition:
\[\begin{gathered}
arc(DE) = \overleftrightarrow {AD} \cdot 2.36 \hfill \\
arc(BC) = \overleftrightarrow {AB} \cdot 1.18 \hfill \\
\end{gathered} \]

Answer 5

Okay, so how do i find the ratio?

Answer 6

please set AD = (2/3) AB into the first expression

Answer 7

you should get this:
\[\begin{gathered}
arc(BC) = \overleftrightarrow {AB} \cdot 1.18 \hfill \\
arc(DE) = \frac{2}{3}\overleftrightarrow {AB} \cdot 2.36 \hfill \\
\end{gathered} \]

Answer 8

I'm confused now

Answer 9

why?

Answer 10

I don't really understand why you do that

Answer 11

let's suppose that AB = 5 feet, what is AD?

Answer 12

3?

Answer 13

Sorry I repeat my reasoning.
Let's suppose AB= 6 feet what is the length of the arc BC?

Answer 14

hint:
arc(BC)= AB * 1.18= ...?

Answer 15

7.08?

Answer 16

ok!
and what is the length of the segment AD?

Answer 17

Hint: AD = 2/3* AB= 2/3 * 6=...?

Answer 18

4?

Answer 19

ok!
and what is the length of the arc DE?
hint:
arc(DE) = AD * 2.36=...?

Answer 20

14.16?

Answer 21

I think 4*2.36= 9.44

Answer 22

Ohhh sorry i got my numbers mixed up >.<

Answer 23

ok! now we know that
arc(BC) = 7.08
and
arc(DE) = 9.44
so what is the ratio:
arc(BC)/ arc(DE) =...?

Answer 24

3/4 ?

Answer 25

that's right!

Answer 26

Is that the answer?

Answer 27

@Michele_Laino ?

Answer 28

yes!

Answer 29

Okay thank you so much for the help :)

Answer 30

thank you!