I make a large equilateral triangle by arranging small equilateral triangle 1cm of the length of one side side by side with no gap nor overlapping.
How many small equilateral triangles do I need to make a large equilateral triangle of 20cm of one side?
How many small equilateral triangles do I need to make a large equilateral triangle of 20cm of one side?
Answer
400 pieces
Solution
In order to make a large equilateral triangle, small equilateral triangles are set out 1 piece, 3 pieces, 5 pieces, 7 pieces, -----.
In order to make the equilateral triangle of 2 cm one side, I need 1 + 3 = 4 pieces and that of 3 cm one side, I need 1 + 3 + 5 = 9 pieces.
That is N × N pieces are needed in order to make the equilateral triangle of N cm one side.
In case one side is 20 cm, I need 20 × 20 = 400 pieces.
In order to make the equilateral triangle of 2 cm one side, I need 1 + 3 = 4 pieces and that of 3 cm one side, I need 1 + 3 + 5 = 9 pieces.
That is N × N pieces are needed in order to make the equilateral triangle of N cm one side.
In case one side is 20 cm, I need 20 × 20 = 400 pieces.
