points a,b,c,and d lie on a straight line in the given order. AC = 25 cm and BD = 46 cm. The ratio of length CD to AB is 5/2. Find the length of line segment BC in cm.

sorry miss the CD part

ahh, that's better

make a sketch of a line and label point A, B, C, and D
using CD : AB = 5:2
label AB = 2x and CD = 5x , giving you the 5:2 ratio

From AC = 25 you can now label BC as 25-2x
From BD = 46 you can label BC as 46-5x

so obviously 25-2x = 46-5x
x = 7
sub back in either of BC expressions, to get BC = 11

thanks :D

given formula fro "c" : A= one half (h b + b c)

The answer is 11!!!😄😄😄😄😄😃😃😃😃😀😀😀😉😉😉😉😉😀😀😀

need more help!!!!!!!!!!!!!!!!!

No problem, I've got it covered! Let's solve the problem step by step.

First, since points A, C, and D lie on a straight line, we can conclude that the total length of AC + CD = AD.

Given that AC = 25 cm and the ratio of CD to AB is 5/2, we can set up the equation: CD/AB = 5/2.

Since AD = AC + CD, we can rewrite this as (AC + CD) / AB = 5/2.

Substituting the known values, we have (25 + CD) / AB = 5/2.

Cross-multiplying, we get 2(25 + CD) = 5(AB).

Simplifying, we have 50 + 2CD = 5AB.

Now, since BD = AB + AD, we can rewrite it as 46 = AB + (AC + CD).

Substituting the known values, we have 46 = AB + (25 + CD).

Simplifying, we have 46 = AB + 25 + CD.

Rearranging the equation, we have AB = 21 - CD.

Now we have two equations: 50 + 2CD = 5AB and AB = 21 - CD.

Substituting AB = 21 - CD into the first equation, we get 50 + 2CD = 5(21 - CD).

Expanding and simplifying, we have 50 + 2CD = 105 - 5CD.

Bringing the CDs to one side, we get 7CD = 55.

Dividing both sides by 7, we find CD = 7.

Now let's substitute the value of CD back into AB = 21 - CD.

AB = 21 - 7.

Simplifying, we have AB = 14.

Since BC = AB + AC, we can calculate BC by substituting the known values: BC = 14 + 25.

Therefore, BC = 39 cm.

So, the length of line segment BC is 39 cm.

No problem! To find the length of line segment BC, we can use the fact that points A, B, C, and D lie on a straight line. Let's break down the information given:

1. AC = 25 cm: This means that the length of line segment AC is 25 cm.

2. BD = 46 cm: This means that the length of line segment BD is 46 cm.

3. The ratio of length CD to AB is 5/2: This implies that CD/AB = 5/2.

Now, let's denote the length of line segment BC as x. Since points A, B, C, and D lie on a straight line, we can represent the lengths of line segments as follows:

AB + BC + CD = AC + BD

Substituting the given values, we have:

AB + x + (5/2)AB = 25 + 46

To simplify, let's first simplify the ratio:

(5/2)AB = (5/2) * AB

Next, we can combine like terms by multiplying:

AB + (5/2)AB = (7/2)AB

So the equation becomes:

(7/2)AB + x = 71

Now, let's rearrange the equation to solve for AB:

AB = (71 - x) * (2/7)

Since we know the ratio of CD to AB is 5/2, we can set up the proportion:

CD/AB = 5/2

Substituting the value of AB, we get:

CD/[(71 - x) * (2/7)] = 5/2

To isolate CD, we can cross-multiply:

CD = 5 * [(71 - x) * (2/7)]

Finally, we have the equation for the length of BC:

BC = CD + BD - AB
= 5 * [(71 - x) * (2/7)] + 46 - AB

Now, substitute the values into the equation and solve for x to find the length of line segment BC.