SOLUTION: ABCD is a trapezoid with midsegment MN. The perimeter of ABCD is 36 yards. The length of AB is 34¯ the length of AD¯. Find the lengths of AB¯, MN, and DC.

Algebra ->  Rectangles -> SOLUTION: ABCD is a trapezoid with midsegment MN. The perimeter of ABCD is 36 yards. The length of AB is 34¯ the length of AD¯. Find the lengths of AB¯, MN, and DC.       Log On


   

Question 1135009: ABCD is a trapezoid with midsegment MN. The perimeter of ABCD is 36 yards.
The length of AB is 34¯ the length of AD¯. Find the lengths of AB¯, MN, and DC.
Shape:
https://gyazo.com/1e610d781083c7b720bf3827751710ea
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Image and video hosting by TinyPic



given:
The perimeter of ABCD is 36+yards.
The length of AB+is 34¯???? the length of AD¯.(I think you put 34 by mistake)
AB+ is probably 3%2F4 the length of AD, I will go with that

MN=%28AB%2BCD%29%2F2
=>AB%2BCD%2BAD%2BBC=36
The line MN is the midline of ABCD. And the segment MN is the midsegment of ABCD.
so,
AM+=+MD=4 => AD=8
BN+=+NC+=5=>BC=10
=>AB%2BCD%2B8%2B10=36
=>AB%2BCD=36-18
=>AB%2BCD=18

MN=%28AB%2BCD%29%2F2
=>MN=18%2F2
=>MN=9

since given that AB+ is 3%2F4 the length of AD=8
=>AB=%283%2F4%298
=>AB=6
then =>6%2BCD=18=>CD=18-6=>CD=12

answer:
MN=9
AB=6
CD=12
AD=8
BC=10
check the perimeter:
AB%2BCD%2BAD%2BBC=36
6%2B12%2B8%2B10=36
36=36