The triangles ABC and DEC are similar triangles. We can prove this using the AA similarity theorem (angle A & angle D are congruent right angles; angle ACB & angle DCE are congruent vertical angles)
Because they are similar triangles, we can form the proportion below and solve for x to get...
AC/CD = BC/CE
2/5 = 3.61/x
2*x = 5*3.61
2*x = 18.05
2*x/2 = 18.05/2
x = 9.025
So EC is roughly 9.025 miles long
This means,
distance from Marc's house to Lewis's house = length of BE
distance from Marc's house to Lewis's house = (length of BC) + (length of EC)
distance from Marc's house to Lewis's house = (3.61) + (9.025)
distance from Marc's house to Lewis's house = 12.635
So the answer is choice D) 12.62 as this is the closest value to 12.635