Answer:
x = 7.5
Step-by-step explanation:
We first labelled the diagram we get
DC = 8
AD = 10
CE = 6
BE = x
∴ AC =AD + DC = 18
∴ BC = BE + ED = x + 6
To Find :
BE = x =?
Solution:
Let DE || AC
In Δ ABC and Δ DEC
∠A ≅ ∠D …………..{corresponding angles ∵ DE || AB }
∠B ≅ ∠E ..............{corresponding angles ∵ DE || AB }
∠C ≅ ∠C ……….....{Reflexive Property}
Δ ABC ~ Δ DEC ….{Angle-Angle-Angle Similarity test}
If two triangles are similar then their sites are in proportion.
On substituting the given values we get
∴
