Answer:
Explanation:
Since line segment EF is parallel to line segment BD, we can use the property that corresponding angles are congruent to set up the following proportion:
EF/BD = FL/BC
Substituting the given values:
EF/4 = 5/12
Cross-multiplying:
EF = 4 x 5/12 = 5/3 cm
We can use the fact that triangles BCD and EFD are similar (having two congruent angles) to set up another proportion:
CD/EF = BC/BD
Substituting the given values:
CD/(5/3) = 12/BD
Solving for CD:
CD = (5/3) x 12/BD = 20/BD cm
We can use the Pythagorean theorem to find the length of BD:
BD^2 = BC^2 + CD^2
Substituting the given values:
BD^2 = 3^2 + 12^2 = 153
Taking the square root of both sides:
BD = sqrt(153) = 3sqrt(17) cm
Substituting this value into the expression for CD:
CD = 20/BD = 20/(3sqrt(17)) = (20/3)sqrt(17) cm
Therefore, the length of line segment CD is (20/3)sqrt(17) cm.