Question #eee14
1 Answer
Sep 27, 2016
20 areal units
Explanation:
Let the altitude meet AB at N.
Let the length of the rectangle, FG=l and the height HN = h.
Then, the area = ( l ) ( h ) areal units.
Let the proportion HF / NB = ( l / 2 ) / 5 = p.
Then, the proportion HN / CN = h / 8 = 1 - p, using proportions in
similar triangles..
Adding,
l / 10 + h / 8 = 1..
Now, the area
lh = 10 h ( 1 - h / 8 ) = f ( h )
For a maximum, f' = 10 ( 1 - h / 4 ) = 0. So, h = 4.
Of course f''= = 5 / 2 < 0.
Corresponding l = 5.
For these l an h, the area lh = 20 is the maximum possible area.
