PSLE Figure 1 shows a triangular card ABC with AC = CB. 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 36 pins were placed at an equal distance of 50 cm apart to hold the cards.
- Find the length of DE.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (36 - 2 x 2) ÷ 2
= (36 - 4) ÷ 2
= 32 ÷ 2
= 16
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 16 - 1
= 15
Length of DE
= 15 x 50
= 750 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 15 - 1
= 14
Number of triangular cards breadthwise = 3
Total number of triangular cards
= 14 + 14 + 3 + 3
= 34
Area of 1 triangular card
=
12 x 50 x 25
= 625 cm
2 Total area of 34 triangular cards
= 34 x 625
= 21250 cm
2 Answer(s): (a) 750 cm; (b) 21250 cm
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