Question

Q11 A line segment DE is drawn
parallel to base BC of AABC which
cuts AB at point D and AC at point E.If
AB= 5xBD and EC=3.2 cm, find the
length of AE.
[4]​

Answer 1

Step-by-step explanation:

AB=5BD

AB−BD=4BD

AD=4BD

or ABAD=54

In △ADE and △ABC,

∠DAE=∠BAC (Common)

∠ADE=∠ABC (Corresponding angles)

∠AED=∠ACB (Corresponding angles)

Thus, △ADE≅△ABC (AAA rule)

Thus, ABAD=ACAE

54=AE+ECAE

5AE=4AE+3.2×4

AE=12.8 cm