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Question
A line segment DE is drawn parallel to base BC of ΔABC which cuts AB at point D and AC at point E. If AB = 5BD and EC = 3.2 cm, find the length of AE.
Solution
In ΔABC
DE || BC
AB = 5BD, EC = 3.2 cm
To find AE
Since, DE || BC
∴ ΔADE ∼ ΔABC
Since a line drawn parallel to one side of triangle divides the other sides proportionality.
∴ `(AD)/(AB) = (AE)/(EC)` ...`{{:(∵ (AB)/(BD) = 5/1),(\implies (BD)/(AB) = 1/5),(AD = AB - BD = 5 - 1 = 4),(∴ (AD)/(DB) = 4/1):}}`
`\implies 4/1 = (AE)/3.2`
`\implies AE = (4 xx 3.2)/1`
= `12.8/1`
= 12.8 cm
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