If CD = 10, CA = 12, and EB = 14, find CE.

Question

△CDE ~ △CBA with ∠CDE ≅ ∠B.

If CD = 10, CA = 12, and EB = 14, find CE.

Answer 1

For similar triangles corresponding sides are in proportion so:

CD/CB = CE/CA

Since CD = 10 and CA = 12 and CB = CE + EB and EB = 14:

10/(CE + 14) = CE/12

cross-multiplying:

CE^2 + 14CE = 120

CE^2 +14CE - 120 = 0

(CE + 20)(CE - 6) = 0

CE = 6