GCSE Maths revision · Geometry and measures

Similar shapes

Foundation and Higher

The idea

Similar shapes have equal angles and every length multiplied by the same scale factor. Find it by dividing a pair of matching sides.

Match the corresponding sides, often by redrawing the shapes the same way round.
Scale factor $= \frac{\text{new length}}{\text{old length}}$ .
Multiply or divide other lengths by it.

Watch out Only compare sides that match: opposite the same angle.

See it worked

Worked exampleNon-calculator2 marks

Rectangle $A$ is 4 cm by 6 cm. Rectangle $B$ is similar to rectangle $A$ . The shorter side of $B$ is 10 cm.

Work out the length of the longer side of rectangle $B$ .

Scale factor $= 10 \div 4 = 2.5$ .
$6 \times 2.5 = 15$

Answer 15 cm

Your turn

Question 1Non-calculator3 marks

At the same time of day, a person 1.8 m tall casts a shadow 2.4 m long, and a tree casts a shadow 16 m long. The person and the tree stand upright on level ground.

Work out the height of the tree.

Question 2Non-calculator4 marks

A photograph is enlarged without changing its proportions. Its width changes from 5 cm to 8 cm and the new height is 32 cm.

(a) Find the original height.

(b) Find the perimeter of the original photograph.

Question 3Non-calculator4 marks

Rectangle A is 3 cm by 7 cm. Rectangle B is similar to rectangle A and has perimeter 60 cm.

(a) Find the scale factor from A to B.

(b) Find the length of the longer side of B.

In past papers

55 official questions in 52 papers since 2017. The latest:

All GCSE Maths past papers

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