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 32 pins were placed at an equal distance of 46 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
= (32 - 1 x 2) ÷ 2
= (32 - 2) ÷ 2
= 30 ÷ 2
= 15
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 15 - 1
= 14
Length of PQ
= 14 x 46
= 644 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 14 - 1
= 13
Number of triangular cards breadthwise = 2
Total number of triangular cards
= 13 + 13 + 2 + 2
= 30
Area of 1 triangular card
=
12 x 46 x 23
= 529 cm
2 Total area of 30 triangular cards
= 30 x 529
= 15870 cm
2 Answer(s): (a) 644 cm; (b) 15870 cm
2