Practice Similarity and central dilation
Similar figures have equal corresponding angles and proportional corresponding lengths.
A scale factor changes lengths, while areas change by its square.
Exercises with solutions
Two figures are similar when all their angles match and all side ratios are equal. The scale factor k says how much longer an image length is: k = image length ÷ original length. Areas grow with k².
Exercise 1
Two triangles are similar. In the first a side is 4 cm, in the second the corresponding side is 10 cm. What is the scale factor?
Show solution and working
k = 2.5
k = 10 cm ÷ 4 cm = 2.5.
Exercise 2
A triangle has sides 3 cm, 4 cm and 5 cm. The similar image has its shortest side 9 cm. How long is the longest side of the image?
Show solution and working
15 cm
k = 9 cm ÷ 3 cm = 3. The longest side is 5 cm · 3 = 15 cm.
Exercise 3
How do the angles change under an enlargement?
Show solution and working
They stay the same
In similar figures all angles are equal. Only the lengths change.
Exercise 4
A triangle has area 6 cm². What is the area of the image for k = 3?
Show solution and working
54 cm²
Areas grow with k². So 6 cm² · 3² = 6 cm² · 9 = 54 cm².
Common mistake
Multiplying the area by the scale factor only once. Areas grow with the square of the scale factor, so for k = 3 with a factor of 9.
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