MathDB

2

Part of 1998 May Olympiad

Problems(2)

ratio of areas within an equilateral triangle

Source: May Olympiad (Olimpiada de Mayo) 1998 L2

9/12/2018
Let ABCABC be an equilateral triangle. NN is a point on the side ACAC such that AC⃗=7AN⃗\vec{AC} = 7\vec{AN}, MM is a point on the side ABAB such that MNMN is parallel to BCBC and PP is a point on the side BCBC such that MPMP is parallel to ACAC. Find the ratio of areas (MNP)(ABC)\frac{ (MNP)}{(ABC)}
geometryareasEquilateral Triangle
max no of different squares by 1998 rectangles 2x3

Source: IV May Olympiad (Olimpiada de Mayo) 1998 L1 P2

9/17/2022
There are 19981998 rectangular pieces 22 cm wide and 33 cm long and with them squares are assembled (without overlapping or gaps). What is the greatest number of different squares that can be had at the same time?
geometryrectanglecombinatoricscombinatorial geometry