et A(p², - p), B(q, q), C(², - r) be the vertices of triangl BC. A parallelogram AFDE is drawn with D, E, and F on th ine segments BC, CA, and AB, respectively. Using calculus how that the maximum area of such a parallelogram

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter11: Introduction To Trigonometry
Section11.4: Applications With Acute Triangles
Problem 45E
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Let A(p²,- p), B(q, q), C(², - r) be the vertices of triangle
ABC. A parallelogram AFDE is drawn with D, E, and F on the
line segments BC, CA, and AB, respectively. Using calculus,
show that the maximum area of such a parallelogram is
(p+q)(q+r)(p-r).
Transcribed Image Text:Let A(p²,- p), B(q, q), C(², - r) be the vertices of triangle ABC. A parallelogram AFDE is drawn with D, E, and F on the line segments BC, CA, and AB, respectively. Using calculus, show that the maximum area of such a parallelogram is (p+q)(q+r)(p-r).
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