Task
19. A. Nine dots are arranged as show in the figure
below, where ABCD is a square. AT=TD, DS=SC, CR=BR, and AP=PQ=QB. A triangle
can be constructed by lining from dot to dot.
At most, there are … different right triangles that one can construct so
that at least one of dots P, Q, R, S and T is it vertex.
Answer :
Answer :
From dot P, Triangles PBR,PBC, PAT, PAD (4)
From dot Q, Trianles QBR, QBC, QAT, QAD (4)
From dot R, Trianles RCS, RCD, RCT, RST, RDT, RTA, RAB, RBT (8)
From dot S, Triangles SDT, SDA, SCB (3)
From dot T, Triangles TDC, TAB (2)
TOTAL = 21 TRIANGLES.
From dot Q, Trianles QBR, QBC, QAT, QAD (4)
From dot R, Trianles RCS, RCD, RCT, RST, RDT, RTA, RAB, RBT (8)
From dot S, Triangles SDT, SDA, SCB (3)
From dot T, Triangles TDC, TAB (2)
TOTAL = 21 TRIANGLES.
19.B. I have placed to numbers 1,2,
and 3 at the vertices of a triangle. Arrange 4, 5, 6, 7, 8, and 9 along the
sides of triangle so that the numbers along each side add to 17!
This is harder: without beibg told
wich numbers to place at the vertices, make similar arrangement of the number
from 1 trough 9, adding to 20 along each side! (several solutions are possible)
Answer
17 = 1-9-3 ; 3-5-7-2 ; 2-8-6-1
20 = 8-1-9-2 ; 2-6-7-5 ; 5-3-4-8
atau 5-4-2-9 ; 9-3-7-1 ; 1-8-6-5
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