Ratio and proportion
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problemSquare Ratio
A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
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problemPythagoras' Comma
Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
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problemEight Ratios
Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.
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problemThe Fastest Cyclist
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
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problemFrom All Corners
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
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problemSame Height
A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?
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problemTelevisual Technology
If a new and an old television have screens of the same area, what is the ratio of their widths?
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problemOrbiting Billiard Balls
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?