PSLE Figure 1 shows a triangular card GHJ with GJ = JH. A number of such cards were arranged along the four sides of a rectangular board. Figure 2 shows part of the arrangement. A total of 60 pins were placed at an equal distance of 10 cm apart to hold the cards.
- Find the length of KL.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (60 - 2 x 3) ÷ 2
= (60 - 6) ÷ 2
= 54 ÷ 2
= 27
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 27 - 1
= 26
Length of KL
= 26 x 10
= 260 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 26 - 1
= 25
Number of triangular cards breadthwise = 4
Total number of triangular cards
= 25 + 25 + 4 + 4
= 58
Area of 1 triangular card
=
12 x 10 x 5
= 25 cm
2 Total area of 58 triangular cards
= 58 x 25
= 1450 cm
2 Answer(s): (a) 260 cm; (b) 1450 cm
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