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A line segment DE is drawn parallel to base BC of ∆ABC which cuts AB at point D and AC at point E. If AB = 5BD and EC = 3.2 cm, find the length of AE.

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Answer

Given,

⇒ AB = 5BD

⇒ AD + BD = 5BD

⇒ AD = 5BD - BD

⇒ AD = 4BD

⇒ ADBD=41\dfrac{\text{AD}}{\text{BD}} = \dfrac{4}{1}.

A line segment DE is drawn parallel to base BC of ∆ABC which cuts AB at point D and AC at point E. If AB = 5BD and EC = 3.2 cm, find the length of AE. Similarity, Concise Mathematics Solutions ICSE Class 10.

Given DE || BC,

by basic proportionality theorem :

∴ADBD=AEEC⇒41=AE3.2⇒AE=4×3.2=12.8 cm.\therefore \dfrac{AD}{BD} = \dfrac{AE}{EC} \\[1em] \Rightarrow \dfrac{4}{1} = \dfrac{AE}{3.2} \\[1em] \Rightarrow AE = 4 \times 3.2 = 12.8 \text{ cm}.

Hence, AE = 12.8 cm

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