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As shown in the figure, AP is the height of △ ABC, point DG is on AB and AC respectively, point E F is on BC, quadrilateral defg is rectangular, AP = h, BC = a, let DG = x, the area of rectangular defg is y, try a, h, X to represent Y
Suppose the intersection of AP and DG is m
∵ defg is a rectangle,
Then de / / BC
So △ ADG ∽ ABC
The two triangles are similar, the ratio of the corresponding side = the ratio of the corresponding height
DG:BC=AM:AP
x：a=AM:h
∴AM=xh/a
So the height of the rectangle is ap-am = (A-X) H / A
The area of rectangle = x × (A-X) H / a = HX HX & # / A
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