Answer:
ED=7.5
Step-by-step explanation:
ΔABC is similar to ΔDEB (they share ∠B, and ∠C=∠D and ∠A=∠E because corresponding angles), so their sides are in ratio:
ED/AC=BD/BC
We can see that BC is twice BD (marked), so we know BD/BC=0.5
ED/AC=BD/BC
ED/15=0.5
ED=7.5
