Making triangle by connecting three vertexes out of eight of the cube.
How many triangles of following (1), (2) and (3) are there?
(1) Equilateral triangle
(2) Right-angled isosceles triangle
(3) Right-angled triangle except (2)
Answer
(1) 8 pieces
(2) 24 pieces
(3) 24 pieces
Solution
( 1) Equilateral triangle can be made when vertexes are connected as shown in the figure below.
How many triangles of following (1), (2) and (3) are there?
(1) Equilateral triangle
(2) Right-angled isosceles triangle
(3) Right-angled triangle except (2)
Answer
(1) 8 pieces
(2) 24 pieces
(3) 24 pieces
Solution
( 1) Equilateral triangle can be made when vertexes are connected as shown in the figure below.
The number is eight which is the same as the number of vertexes of the cube .
( 2 ) In each face of the cube four isosceles right triangles can be made.
( 2 ) In each face of the cube four isosceles right triangles can be made.
Total is 4 × 6 = 24 pieces.
( 3 ) Total number of right triangles that can be made by connecting vertexes as shown in the figure below is 4 × 6 = 24 pieces.
( 3 ) Total number of right triangles that can be made by connecting vertexes as shown in the figure below is 4 × 6 = 24 pieces.
