A, B, C and D are four points on a line such that AB:AC = 7:10, and BD:CD = 9:2. If CD = 9 cm, what is the length, in cm, of AB?
A) 49 B) 64 C) 54.25 D)73.25 E)70
Let
AB=7m
BC=3m
Now let
BC=7n
CD=2n
Now, CD=9, so n=9/2
BC=7*9/2 = 63/2 = 3m
so m = 21/2, making
AB = 7m = 7*21/2 = 147/2 = 73.5
Is there a typo, or did I make a mistake?
D should be 73.5, so you are correct
Well, I have to admit, these points on a line definitely know how to keep things interesting! Let's have some fun with this problem, shall we?
Since AB:AC = 7:10, we can assign values to AB and AC. Let's say AB = 7x and AC = 10x, where x is a mysterious variable that we'll figure out later. Hang on to your funny bone!
Now let's move on to BD:CD = 9:2. We know that CD = 9 cm, so let's find out what BD is. In this case, let's assign BD = 9y and CD = 2y. Who doesn't enjoy a little mystery, right?
Since we're given CD = 9 cm, we can substitute it in our equation: 2y = 9. Solving for y, we find that y = 4.5. Now let's find out what AB is.
Remember that AB = 7x, so let's use the ratio BD:CD = 9:2 to find x. We get BD/CD = AB/AC. Substituting the values we know, we get (9y)/(2y) = (7x)/(10x).
By canceling out the y and x, we find that 9/2 = 7/10. Whoops! Looks like something's gone a bit haywire. This equation is definitely not a laughing matter.
There seems to be an error, which means there might be a typo in the problem or perhaps another piece of information is missing. Without any additional information, it's impossible to determine the length of AB.
So, unfortunately, it looks like you've stumped me this time. But hey, at least we had some laughs along the way! Keep those questions coming, and I'll do my best to keep you entertained.
To find the length of AB, we first need to find the length of AC.
We are given that AB:AC = 7:10. We can set up a proportion using this information:
AB/AC = 7/10
Cross-multiplying, we get:
10 * AB = 7 * AC
Next, we need to find the length of BD.
We are given that BD:CD = 9:2. Since CD = 9 cm, we can set up a proportion:
BD/CD = 9/2
Cross-multiplying, we get:
2 * BD = 9 * CD
Since CD = 9 cm, we have:
2 * BD = 9 * 9
Simplifying, we get:
2 * BD = 81
Now, let's find the length of AC.
Substituting the value of AC from the first proportion into the equation, we get:
10 * AB = 7 * AC
10 * AB = 7 * 81
10 * AB = 567
Dividing both sides by 10, we get:
AB = 567/10
Finally, to find the length of AB, we divide 567 by 10:
AB ≈ 56.7 cm
Therefore, the length of AB is approximately 56.7 cm.
Looking at the answer choices, we see that none matches exactly with 56.7 cm. However, option C) 54.25 cm is the closest.