1

Part of 1996 May Olympiad

Problems(2)

minimal sum of areas of triangles insides a rectangle

Source: May Olympiad (Olimpiada de Mayo) 1996 L2

ABCD

be a rectangle. A line

r

moves parallel to

AB

and intersects diagonal

AC

, forming two triangles opposite the vertex, inside the rectangle. Prove that the sum of the areas of these triangles is minimal when

r

passes through the midpoint of segment

AD

geometryrectangleareas

dividing a right trapezoid in equal areas

Source:

ABCD

) has a rectangular trapezoidal shape. The angle in

A

90^o

AB

30

AD

20

DC

measures 45 m. This land must be divided into two areas of the same area, drawing a parallel to the

AD

side . At what distance from

D

do we have to draw the parallel? https://1.bp.blogspot.com/-DnyNY3x4XKE/XNYvRUrLVTI/AAAAAAAAKLE/gohd7_S9OeIi-CVUVw-iM63uXE5u-WmGwCK4BGAYYCw/s400/image002.gif

geometrytrapezoidequal area