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.