Answer:
The length of legs lm, mn, and lk is 32 while that of kn is 36.
Step-by-step explanation:
As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk
This leads the two set of legs such as
(lm)/(kn)=(8)/(9)
Or this could be written as
lm=8x\nkn=9x
Now the remaining two sides are given as
lk=lm as this form an isosceles triangle so
lk=8x
Similarly
mn=lm\n
Or
mn=8x
Now the perimeter is given as
\text{perimeter}=lm+mn+kn+lk\n
Here perimeter is given as 132 so this gives:
\text{perimeter}=lm+mn+kn+lk\n132=8x+8x+8x+9x\n132=33x\nx=(132)/(33)\nx=4
So the four legs are of length as given below:
lm=8x=8* 4=32\nmn=8x=8* 4=32\nlk=8x=8* 4=32\nkn=9x=9*4=36
So the length of legs lm, mn, and lk is 32 while that of kn is 36.
