Question

will make brainiest if possible need explanation too :)

The points A, B, C and D lie in order on a straight line.
AB : BD = 1:4
AC: CD = 7:13
Work out AB : BC: CD
Give your answer in its simplest form.

Answer 1

Answer:

AB : BC : CD = 4 : 3 : 13

Step-by-step explanation:

AC:CD = 7:13

AC+CD = 7+13 = 20

AB:BD = 1:4

AB = (20 / (1+4))*1 = 4   ... 1/5 0f 20

BD = (20 / (1+4))*4 = 16  ... 4/5 of 20

BC = BD - CD = 16-13 = 3

AB : BC : CD = 4 : 3 : 13

Answer 2

Lines can be divided in ratios

The ratio is: AB : BC : CD = 4 : 3 : 13

The given parameters are:

$\mathbf{AB : BD = 1:4}$

$\mathbf{AC: CD = 7:13}$

Using unit ratio, we have:

$\mathbf{AC+CD = 7+13}$

$\mathbf{AC+CD = 20}$

This gives

$\mathbf{AD = 20}$

$\mathbf{AB : BD = 1:4}$ implies that:

$\mathbf{AB = \frac{1}{1 + 4} \times AD}$

$\mathbf{AB = \frac{1}{5} \times 20}$

$\mathbf{AB = 4}$

Also, we have:

$\mathbf{BD = \frac{4}{1 + 4} \times AD}$

$\mathbf{BD = \frac{4}{5} \times 20}$

$\mathbf{BD = 16}$

AC : CD = 7 : 13 means that:

CD = 13

So, we have:

$\mathbf{BC + CD = BD}$

This gives

$\mathbf{BC + 13 = 16}$

Subtract 13 from both sides

$\mathbf{BC = 3}$

So, we have:

$\mathbf{AB = 4}$

$\mathbf{BC = 3}$

CD = 13

Hence, the ratio is:

AB : BC : CD = 4 : 3 : 13

Read more about line ratios at:

https://brainly.com/question/19608914