I do not understand this at all. Can someone please show all the steps sp I am able to comprehend:
Four points are on a line segemnts, as shown. If AB:BC=1:2 and BC:CD=8:5, then AB:BD equals what?
Assume CD = 1
Then, BC = 8.5. and AB == 10.2.
Therefore, AB/BD = 10.2/9.5 = 1.07368.
Assume CD to be anything you want and follow the same steps which will lead you to the same result.
To understand how to solve this problem, let's break it down step by step:
1. Assume a value for CD: In this case, let's assume CD = 1.
2. Use the given ratios to find the lengths of the other line segments:
- Since AB:BC = 1:2, and BC is known (8.5, based on the assumption in Step 1), we can calculate AB:
AB = BC/2 = 8.5/2 = 4.25
- Similarly, since BC:CD = 8:5 and CD is known (1, based on the assumption in Step 1), we can calculate BC:
BC = CD * (8/5) = 1 * (8/5) = 1.6
3. Find the length of AB:BD:
- To find AB:BD, we need to know the length of BD. Let's assume BD = x.
- Now we have AB (4.25) and BD (x), so we can calculate AB:BD as AB/BD = 4.25/x.
4. Substituting values and solving the equation:
- From Step 2, we know that AB = 4.25 and BC = 1.6.
- We can calculate CD using BC:CD = 8:5 as CD = BC * (5/8) = 1.6 * (5/8) = 1.
- Now, let's substitute the values into the equation AB/BD = 4.25/x:
4.25/x = 1.07368 (rounded to five decimal places)
5. Solve for x:
- To solve for x, cross-multiply:
4.25 * x = 4.25 * 1.07368
x = 4.56702 (rounded to five decimal places)
6. Calculate AB:BD:
- Now that we have found BD (x = 4.56702), we can calculate AB:BD as AB/BD = 4.25/4.56702 = 0.93153 (rounded to five decimal places).
So, the ratio AB:BD is approximately 0.93153 (or you can simplify it as 1:1.074, rounded to three decimal places), regardless of the value you assume for CD.