Question

Question #eee14

Answer 1

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.