Question

DE
is parallel to start overline, A, B, end overline
AB
. C, E, equals, 5CE=5, D, A, equals, 3, point, 8DA=3.8, and E, B, equals, 3EB=3. Find the length of start overline, C, D, end overline
CD
. Round your answer to the nearest tenth if necessary.
A
B
C
E
D

CD = what

Answer 1

Treat A, B, C as a triangle with D on AC and E on BC and DE ∥ AB. Then triangles CDE and CAB are similar, so

CD/(CD + AD) = CE/(CE + EB).

Substitute AD = 3.8, CE = 5, EB = 3:
CD/(CD + 3.8) = 5/8.

Solve: 8·CD = 5·(CD + 3.8) → 8CD = 5CD + 19 → 3CD = 19 → CD = 19/3 ≈ 6.333…

Rounded to the nearest tenth: 6.3.