Answer:
perimeter = 34
Explanation:
given EP = FP and GQ = FQ , then
4y + 2 = 2x ( subtract 2x from both sides )
4y - 2x + 2 = 0 ( subtract 2 from both sides )
4y - 2x = - 2 → (1)
and
4y + 4 = 3x - 1 ( subtract 3x from both sides )
4y - 3x + 4 = - 1 ( subtract 4 from both sides )
4y - 3x = - 5 → (2)
Solve the 2 equations simultaneously
multiplying (2) by - 1 and adding to (1) will eliminate y
- 4y + 3x = 5 → (3)
add (1) and (3) term by term to eliminate y
0 + x = 3
x = 3
substitute x = 3 into (1) and solve for y
4y - 2(3) = - 2
4y - 6 = - 2 ( add 6 to both sides )
4y = 4 ( divide both sides by 4 )
y = 1
thus x = 3 and y = 1
PQ = x + 2y = 3 + 2(1) = 3 + 2 = 5
PQ is the mid segment of Δ EFG and is half the length of GE , then
GE = 2 × 5 = 10
the perimeter (P) is the sum of the 3 sides , that is
P = FQ + QG + GE + EP + PF
= 3x - 1 + 4y + 4 + 10 + 4y + 2 + 2x
= 5x + 8y + 11
= 5(3) + 8(1) + 11
= 15 + 8 + 11
= 34