Plans of houses and instructions for assembling shelves, etc., often come in the form of scale diagrams. each length on the diagram represents a length relating to the real house, the real shelves, etc. often a scale is given on the diagram so that you can see length on the diagram represents a standard length, such as a metre, on the real object. length always represents the same standard length, wherever it is on the diagram and in whatever direction.

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other lengths may represent fractions or multiples of standard length. thus, lengths are half as long on the diagram represent lengths are half as long in reality; lengths are twice as long on the diagram represent lengths are twice as long in reality; and so on.

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scale diagrams are often drawn on a square grid. it is then possible to count squares on the grid rather than measure lengths on the diagram. care must be taken with either method: the ends of a length may fall between the marks on the ruler, or the grid lines may not be equally spaced.

example 1

below is a scale plan of a bathroom. answer the questions listed below the plan. you might want to show the ruler and then drag it to make your measurements.

the background squares show the length representing 1 m.

click on 'reveal answer' for a detailed solution.

example 2

(a) the scale on a diagram is such that 2 cm represent 1 m. what lengths do 6 cm, 0.2 cm, 3 cm, 3.6 cm and 0.5 cm represent?

(b) a window is 2.3 m wide and 1.4 m . draw a scale diagram of the window, using a scale in 2 cm represent 1 m.