klm ~ nop ??

Question

Need help on this problem

Have to find the measure of the missing side

k=24, l=30, m=15, n=16

i don' get it at all
Can you tell me the answer to this problem?
and show how you did it?
so that i can have a clue on how to do it for allthe other problems similar to this one.
thanks
=]

Answer 1

Though you don't say so, I'm guessing that you are referring to similar triangles, right? If so, you can set up proportions to find any missing sides.

Since klm~nop, you have proportions as such:

k/n = l/o = m/p

We're given k, l, m, so just fill them in:

24/16 = 30/o

24 o = 16(30)
o = 20

24/16 = 15/p
24p = 16(15)
p = 10

That's it, now we know all the sides. :)

Answer 2

A picture would be nice but I'm guessing you are doing this by a triangle... But either way, this problem is possible so let's see here...

This ~ tilda sign shows you're doing Similarity, and that's key...

The first thing you need to know is the way the structure is written

klm ~ nop

k is similar to n
l is similar to o
m is similar to p

Now the key thing you want to look here is called "a ratio"... If you at least have a set of similarties that are both given to you, then you can divide the two similarties to be your ratio. Watch what I mean... I'll use this same similarity statement I typed above and I'll plug in the given variables of [k=24, l=30, m=15, n=16]

24 is similar to 16
30 is similar to o [o and p are missing sides]
15 is similar to p

Oh look! The top row has both numbers given, so divide those two numbers according to your 'klm ~ nop', in this case, work backwards and just do it by n/k

16/24 = 2/3 (Simplified by dividing by 8)

So, now that you know 2/3 is your "ratio", all you have to do to that ratio is to multiply the middle and bottom rows to get your remaining two variables, o and p.

30 * (2/3) = 20 = o
15 * (2/3) = 10 = p

Basically, this is what you can do:

1) Notice the similarity such as

(K)lm ~ (N)op (first letter 1st side is similar to first letter 2nd side!)

k(L)m ~ n(O)p (second letter 1st side is similar to 2nd side 2nd letter's side)

kl(M) ~ no(P) third letter 1st side is similar to third letter second letter side

2) Organize the problem

k=
l=
m=

n=
o=
p=

3) Important : Do the ratio of the second side over the first side, always.

Like n/k works, and o/l works, etc. Get your ratio.

4) Multiply your ratio out to get the other missing sides!

Answer 3

Remember that by definition, if two triangles are similar, then the ratio of each side to the corresponding side of the other triangle is the same. In other words, we have n/k = o/l = p/m. So solving for o:

o = nl/k = 16*30/24 = 20

And for p:

p = mn/k = 15*16/24 = 10

And we are done.