PSLE Figure 1 shows a triangular card LMN with LN = NM. 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 46 pins were placed at an equal distance of 26 cm apart to hold the cards.
- Find the length of PQ.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (46 - 2 x 3) ÷ 2
= (46 - 6) ÷ 2
= 40 ÷ 2
= 20
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 20 - 1
= 19
Length of PQ
= 19 x 26
= 494 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 19 - 1
= 18
Number of triangular cards breadthwise = 4
Total number of triangular cards
= 18 + 18 + 4 + 4
= 44
Area of 1 triangular card
=
12 x 26 x 13
= 169 cm
2 Total area of 44 triangular cards
= 44 x 169
= 7436 cm
2 Answer(s): (a) 494 cm; (b) 7436 cm
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