Question

Points A, B, C, and D
lie on a line segment
as shown. If AB:BC is
1:3 and BC:CD is 7:5,
then find AC:BD.​

Answer 1

Answer:

3.8

Step-by-step explanation:

A B=B C AND B C=C D then AC =B D is 3.8

Answer 2

Given:

AB:BC=1:3

BC:CD=7:5

To find:

AC: BD

Solution:

The value of AC: BD is 7:9.

We can find the ratio by following the given steps-

Let us assume that the length of the line segment is X units.

We know that the line segment is divided by A, B, C, D in the given ratios.

Since AB: BC=1:3 and BC: CD=7:5, we will find the value of AB: BC: CD.

So, we will multiply AB: BC with 7 and BC: CD with 3 to obtain the ratio of all three lengths.

On multiplying, we get

AB:BC=7:21 and BC:CD=21:15

Now, AB:BC:CD=7:21:15

The length of AB=7X

The length of BC=21X

The length of CD=15X

AC=AB+BC

=7X+21=28X

BD=BC+CD

=21X+15X=36X

We will find the ratio of AC and BD by dividing their values.

AC/BD=28X/36X

AC/BD=7/9

AC: BD=7:9

Therefore, the value of AC: BD is 7:9.