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Question
In ΔABC, MN is drawn parallel to BC. If AB = 3.5cm, AM : AB = 5 : 7 and NC = 2cm, find:
(i) AM
(ii) AC
Solution
(i) `"AM"/"AB" = (5)/(7)`
∵ AB = 3.5cm
∴ AM = `(5 xx "AB")/(7)`
⇒ AM = `(5 xx 3.5)/(7)`
⇒ AM = 2.5cm.
(ii) Since MN || BC and `"AM"/"MB" = "AN"/"NC"`
∵ AB = 3.5cm; AM = 2.5cm
∴ MB
= AB - AM
= 3.5 - 2.5
= 1cm
⇒ `"AM"/"MB" = "AN"/"NC"`
⇒ `(2.5)/(1) = "AN"/(2)`
⇒ AN = `(2.5 xx 2)/(1)` = 5cm
Now,
AC = AN + NC
⇒ AC
= 5 + 2
= 7cm.
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