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Comparing Sizes

Comparing Sizes

Measurements can be compared using a ratio. A door in a very old building might be 1.5m high; a door in a new building would be 2.0m high. The ratio old door:new door is 1.5:2.0, or 1:1.33,

Take care when translating ratios from a linear measurement to an area. Compare a small rectangle 2cm long by 3cm high with a larger rectangle 6cm long and 9cm high. The ratio for the lengths and heights are 1:3. However, the area of the first rectangle is 6cm2, and for the second 54 cm2. For the area, this is a ratio of 6:54, or 1:9. The area ratio increases by the square of the linear ratio.

Similarly, compare a cube 1cm by 1cm by 1cm with a cube 5cm by 5cm by 5cm. The volume of the small cube is 1 x 1 x 1 = 1cm3. the volume of the larger cube is 5 x 5 x 5 = 125cm3. The volume ratio increase by the cube of the linear ratio.

Example 1

The distance between the two rails of a railway line is normally 1432mm. The distance between two rails of a model railway line is 16.5mm. What is the ratio of the distance between the rails as model : real?

Divide both 16.5 and 1432 by 16.5 for 1:87 (rounded to the nearest integer).

Answer: 1 : 87

Example 2

On a drawing, a field is 50cm long and 150cm wide. The actual field is 120m by 360m wide. What is the ratio of the areas?

Area of drawing is 0.5m by 1.5m = 0.75 m2.

Area of field is 120 x 360 = 432002.

Ratio of the areas are 0.75:43200; divide both numbers by 0.75 for 1:57600.

Answer: 1 : 57600