Perimeter | Finding a missing length

The diagram shows a rectangle and a square.

The perimeter of the rectangle is the same as the perimeter of the square.

Work out the length of one side of the rectangle.

Solution.........perimeter, p, is the sum of lengths around a shape


rectangle, p = 8+8+2+2 = 20 cm

square, s = 20/4 = 5 cm ....4 is the number of equal sides in a square

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Students note
- showing a clear working out will result in awarding of full marks
- key to getting this question right is knowing how to find perimeter and 4 sides of a square are equal.

Teachers note
- students should know the formulae p = 2( l + w) and p = 4s, for rectangle and square respectively. But, I think the best strategy is to show students the concept, not formula, as the concept can be used in both regular and irregular shapes. Remembering to use formulae can create confusion in contextual exam setting if a student can not recall them easily.
 

Perimeter | Adding the lengths by collecting like terms

In the diagram, all measurements are given in centimetres.

All angles are right angles.

Show that the perimeter of the shape can be written as 2(3x + 5).

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Solution

perimeter = side 1 + side 2 + side 3 + ...... (two sides are missing)

                = 2x + x + 3 + 2 + horizontal missing side + vertical missing side

                = 2x + x + 3 + 2 + 2x + 3 + x + 2

                = 6x + 10

                = 2(3 + 10) ......you've got to factorise to show

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Note: to get 4 full marks for this question, student must show (by calculation).