A, B, C , D and E are points on a line segment such that AE= 10 cm , AB = 3 cm and DE = 2 cm. If C is the midpoint of AE.
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Answer:
Step-by-step explanation:
AB=5BD
AB−BD=4BD
AD=4BD
or
AB
AD
=
5
4
In △ADE and △ABC,
∠DAE=∠BAC (Common)
∠ADE=∠ABC (Corresponding angles)
∠AED=∠ACB (Corresponding angles)
Thus, △ADE≅△ABC (AAA rule)
Thus,
AB
AD
=
AC
AE
5
4
=
AE+EC
AE
5AE=4AE+3.2×4
AE=12.8 cm
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