Question

PLEASE PLEASE PLEASE HELP ME

Answer 1

Answer:

CE = 17

Step-by-step explanation:

∵ m∠D = 90

∵ DK ⊥ CE

∴ m∠KDE = m∠KCD⇒Complement angles to angle CDK

In the two Δ KDE and KCD:

∵ m∠KDE = m∠KCD

∵ m∠DKE = m∠CKD

∵ DK is a common side

∴ Δ KDE is similar to ΔKCD

∴ $\frac{KD}{KC}=\frac{DE}{CD}=\frac{KE}{KD}$

∵ DE : CD = 5 : 3

∴ $\frac{KD}{KC}=\frac{5}{3}$

∴ KD = 5/3 KC

∵ KE = KC + 8

∵ $\frac{KE}{KD}=\frac{5}{3}$

∴ $\frac{KC+8}{\frac{5}{3}KC }=\frac{5}{3}$

∴ $KC + 8 = \frac{25}{9}KC$

∴ $\frac{25}{9}KC - KC=8$

∴ $\frac{16}{9}KC=8$

∴ KC = (8 × 9) ÷ 16 = 4.5

∴ KE = 8 + 4.5 = 12.5

∴ CE = 12.5 + 4.5 = 17