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Similarity – practice for Year 9

Sample questions on Similarity with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Year 9
Curriculum area
Geometry and measures

Question types: Similar triangles

Rule: Similarity

Similar shapes have all their sides enlarged (or reduced) the same way, by the scale factor k.

k = new side ÷ matching old side. Multiply lengths by k, areas by k².

Example: a = 6 cm, a' = 18 cm: k = 3, so c = 8 cm → c' = 24 cm

Watch out: With sides three times as long, the area is 9 times bigger, not 3 times.

Sample questions

  1. Question 1 Easy

    Triangle ABC has sides a = 5 cm, b = 8 cm and c = 6 cm. Triangle A'B'C' is similar to it and its side a' is 10 cm. Work out the length of side c'.

    Show the solution
    Answer: 12 cm

    How it works: k = 10 ÷ 5 = 2; c' = 2 × 6 = 12 cm

  2. Question 2 Normal

    An upright pole 1.5 m tall casts a shadow 4 m long. At the same moment a tree casts a shadow 20 m long. How tall is the tree?

    Show the solution
    Answer: 7.5 m

    How it works: The pole–shadow and tree–shadow triangles are similar: 20 ÷ 4 = 5; 1.5 × 5 = 7.5 m

  3. Question 3 Hard

    The sides of triangle ABC are 3 times as long as the matching sides of triangle KLM. The area of KLM is 12 cm². What is the area of ABC?

    Show the solution
    Answer: 108 cm²

    How it works: Areas of similar shapes are in the ratio k² = 9: 12 × 9 = 108 cm²

Related topics

All Maths topics

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