Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on DE. Show that shaded area is less than or equal to one-fourth of the area of the entire triangle. Where α(BDF) + α(CEF) = 1 4α(ABC) if and only if points D and E are the midpoints of AB and AC, respectively.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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 Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on
DE. Show that shaded area is less than or equal to one-fourth
of the area of the entire triangle. Where α(BDF) + α(CEF) = 1
4α(ABC) if and only if
points D and E are the midpoints of AB and AC, respectively.

23.4 Let ABC be any triangle, let DE be a
line parallel to the base, and let F be
any point on DE. Show that the area of
the union of the two triangles DBF and
ECF is less than or equal to one-fourth
the area of the whole triangle, with
equality if and only if D and E are the
midpoints of AB and AC.
B
D
A
F
E
E
C
Transcribed Image Text:23.4 Let ABC be any triangle, let DE be a line parallel to the base, and let F be any point on DE. Show that the area of the union of the two triangles DBF and ECF is less than or equal to one-fourth the area of the whole triangle, with equality if and only if D and E are the midpoints of AB and AC. B D A F E E C
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