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Question 15b

Video explanation ↓

Figure A is a square formed using 2 identical tiles. Figure B is a rectangle formed by rearranging the tiles. The area of Figure A is 81 m². Figure C shows a rectangular path formed by using the tile pattern of Figure B. The path is continuous and completely covered. It has an area of 2106 m². What is the perimeter of the path? (4 marks)

Question 15b diagram

Answer: 714 m

Workings

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figure A is a square, which means they have equal sides

area of square = side x side

area of square = 81 m²

what same number multiple by itself gives 81?

9 x 9 = 81

side of square = 9m

since the tiles small side creates 2u

2u = 9m 1u = 9 ÷ 2 = 4.5m 3u = 9 + 4.5 = 13.5m

figure B area is the same as figure A, since they both have the same tiles (81m²)

number of figure B tiles → 2106 ÷ 81 = 26

path length → 26 x 13.5 = 351m

path breadth → area of B ÷ length of B = 81 ÷ 13.5 = 6m

path perimeter → 2 x path length + 2 x path breadth = 2 x 351 + 2 x 6 = 714m

Video explanations

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