SOLUTION: In parallelogram MATH , the ratio of MA to AT is 4:2. Find MA if thr perimeter is 60

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Question 719165: In parallelogram MATH , the ratio of MA to AT is 4:2. Find MA if thr perimeter is 60
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The perimeter of a parallelogram is P=2%28a+%2B+b%29 where a and b are the lengths of adjacent sides.
you are given: a=MA, b=AT, and a%3Ab=4%3A2......eq. 1
P=60....eq. 2
from a%3Ab=4%3A2......eq. 1, we have 2a=4b...=>...a=4b%2F2..=>...a=2b...plug it in 60=2%28a+%2B+b%29
60=2%282b+%2B+b%29, and solve for b
60=2%283b%29
60=6b
highlight%2810=b%29
now find a
a=2b
a=2%2A10
highlight%28a=20%29
check if their ratio is 4%3A2
20%3A10=4%3A2

%2820%2F5%29%3A%2810%2F5%29=4%3A2

4%3A2=4%3A2...this verifies our answer