Answer:
38 units
Step-by-step explanation:
EP = FP , then
4y + 2 = 2x → (1)
GQ = FQ , then
4y + 4 = 3x - 1 ( subtract 4 from both sides )
4y = 3x - 5 → (2)
substitute 4y = 3x - 5 into (1)
3x - 5 + 2 = 2x ( subtract 2x from both sides )
x - 3 = 0 ( add 3 to both sides )
x = 3
substitute x = 3 into (1)
4y + 2 = 2(3) = 6 ( subtract 2 from both sides )
4y = 4 ( divide both sides by 4 )
y = 1
Then
EP = 4y + 2 = 4(1) + 2 = 4 + 2 = 6 = FP
GQ = 4y + 4 = 4(1) + 4 = 4 + 4 = 8 = FQ
PQ is a midsegment and is half the length of EG
PQ = x + 2y = 3 + 2(1) = 3 + 2 = 5 , so
EG = 2 × 5 = 10
Then summing the parts for perimeter (P)
P = 6 + 6 + 8 + 8 + 10 = 38
