MathDB

The picture below shows the way Juan wants to divide a square field in three regions, so that all three of them share a well at vertex

B

. If the side length of the field is

60

meters, and each one of the three regions has the same area, how far must the points

M

and

N

be from

D

?
Note: the area of each region includes the area the well occupies.
[asy] pair A=(0,0),B=(60,0),C=(60,-60),D=(0,-60),M=(0,-40),N=(20,-60); pathpen=black; D(MP("A",A,W)--MP("B",B,NE)--MP("C",C,SE)--MP("D",D,SW)--cycle); D(B--MP("M",M,W)); D(B--MP("N",N,S)); D(CR(B,3));[/asy]

1

Problems(1)