PSLE Figure 1 shows a triangular card JKL with JL = LK. 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 38 pins were placed at an equal distance of 22 cm apart to hold the cards.
- Find the length of MN.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (38 - 2 x 2) ÷ 2
= (38 - 4) ÷ 2
= 34 ÷ 2
= 17
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 17 - 1
= 16
Length of MN
= 16 x 22
= 352 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 16 - 1
= 15
Number of triangular cards breadthwise = 3
Total number of triangular cards
= 15 + 15 + 3 + 3
= 36
Area of 1 triangular card
=
12 x 22 x 11
= 121 cm
2 Total area of 36 triangular cards
= 36 x 121
= 4356 cm
2 Answer(s): (a) 352 cm; (b) 4356 cm
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