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1. i) AD=3.6 AB=10 AE =4.6 EC=? AC=?
ii)AB=13.3 AC=11.9 EC=5.1 AD=?
iii) AD=4 DB=7 AC=6.6 AE=?
iv) AD=8 AB=15 EC=3.5 AE=?
Step-by-step explanation:
i)according to areas similarity therom:
(AD/AB)^2=(AE/AC)^2
3.6/10=4.6/AC
AC= 4.6×10/3.6
AC=46/3.6
AC=12.7cm
AC=AE+EC
12.7=4.6+EC
EC=12.7-4.6
=8.1cm
ii)DB/AB=EC/AC
DB/13.3=5.1/11.9
DB=5.1×13.3/11.9
DB=67.83/11.9
DB=5.7cm
AB=AD+DB
AD=AB-DB
AD=13.3-5.7
AD=7.6cm
iii)AB=AD+DB
AB=4+7
AB=11cm
AD/AB=AE/AC
4/11=AE/6.6
AE=4×6.6/11
AE=4×0.6
AE=2.4cm
iv)AB=AD+DB
15=8+DB
DB=15-8
DB=7cm
AD/DB=AE/EC
8/7=AE/3.5
AE=8×3.5/7
AE=8×0.5
AE=4cm.
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