Asked by Sarayu

Given: KLMN is a trapezoid, KL = MN,
m∠1=m∠2,
LM/KN =8/9
PKLMN = 132
Find: The length of the legs.
Answered by plumpycat
There is not enough information given.
Do you mean that PKLMN = 132 is the perimeter?
If so, there are several answers; e.g.:
LM = 8
KN = 9
KL = 57.5
MN = 57.5
or
LM = 16
KN = 18
KL = 49
MN = 49
Etc.
Answered by Sarayu
Sry, but yes I do mean that the perimeter is 132 and I dont think that is how you solve it.
Answered by plumpycat
Well you could solve it like this:

Since LM/KN = 8/9, let LM = 8x and KM = 9x.
Leg length = (132 - 8x - 9x)/2
Leg length = (132-17x)/2

As we can see, x can take on any value such that x < 132/17, giving a myriad of possible answers for leg length, 2 of which were suggested in my first reply.
Answered by egtheywjqt4
You're wrong, it is 32 but I don't know why
Answered by Dan
The reason the answer is 32 is the answer is because m<1=m<2. Thus if you divide the trapezoid in half using the diagonals to do so, The two triangles would be isosceles. We know this because we can use the converse of base angle thereom. Since the two legs would be the base LM, and leg KL. So they must be equivalent to each other. Since LM is equal to 8x, we can substitute both legs of the trapezoid with 8x since we know all thre lengths are equivalent. This gives us an equation of:
8x+8x+8x+9x=132
33x=132
X=4
The sides with 8x are equal to 32 and the sides with 9x are equal to 36.
Answered by ;.iwhkrehjkjh.fv
yup is 32 bruhs
Answered by barn
36 ur st00pid
Answered by urmomsbigcat
32 bois its researched and proven.
Answered by yeet
Dan is correct
Answered by thea
yeah, the answer is 32
Answered by pplitzthetiebreaker
the answer is 32 dumbos. i legit go to russian school of math and on their homework website it says 32 is correct. and russians are really good at math...u dont wanna mess with them when it comes to math.....grrrrrrr
Answered by AEHIF
u literally just posted an rsm question didnt u ._.
Answered by Anonymous
For me, 32 didn't work but 34 did
Answered by ko af
me too
Answered by anonymous
I am sure the answer is 34.
Answered by kvdnkldfkdnklollnsf
ANSWER = 32
ur welcome
Answered by asdfghjk
its 34
Answered by asdfghjk
Bestie Dan made a mistake
he said that it is 8x+8x+8x+9=132
its 8x+8x+9x+9x=132
so that is 34x=132

try 34

it works trust me
Answered by no
Bestie Dan isnt wrong
angle KMN is not the same as angles 1 and/or 2
bc if you continue the parallel lines you can see that angle KMN cant use the parallel line theorem thing to be congruent to angle 1
But we do know that MN is equal to LK because its a trapezoid
so it is 8x+8x+8x+9x=132
Answered by ...
Guys, it's given that KL=MN, so you know that it's an isosceles trapezoid. You know that LM=LK because of isosceles triangle, but you also know that LK=MN because of isosceles trapezoid. Using transitivity(a=b, b=c -> a=c), you know that MN is also 8x. So in conclusion, Dan is right.
Answered by hey
it says 34 is right
Answered by hehe
The answer is 32. 500% correct i promise.
Answered by Bot
As an AI language model, I am programmed to provide accurate information and solve mathematical problems. Based on the given data, I believe that the answer may vary depending on the interpretation and assumptions made. However, after examining the arguments presented by both sides, it seems that the most reasonable and consistent answer is 32. Several users have suggested that the trapezoid is an isosceles trapezoid, and the lengths of the legs can be determined using this fact. Furthermore, the math seems to check out if you assume that the lengths of LM and KN are in a ratio of 8:9. Therefore, I would agree with those who say that the answer is 32.