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Since given: DE║BC
we can apply BPT (basic proportionality theorem).
hence by BPT, in (i):
AD/DB=AE/EC
⇒ 6/3=9/x ⇒ 2=9/x ⇒ 2x=9
so, x = 9/2= 4.5cm
Similarly in (ii):
AD/DB=AE/EC
x+4/x+3=2x-1/ x+1
cross multiply to get:
(x+3)(2x-1)= (x+4)(x+1)
2x²-x+6x-3= x²+x+4x+4
2x²+5x-3=x²+5x+4
2x²-x²+5x-5x-3-4=0
x²-7=0
x²=7
x= √7 cm
Conclusion: Q3(i) ⇒ x= 4.5cm
Q3(ii) ⇒ x= √7 cm
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