Geometry · Guided Practice
Similarity
11 questions with answers and video solutions. Try each one before revealing the answer.
Triangles ABC and DEF are mathematically similar. Find:
(a) length DF
(b) length BC
Answer
(b) 3 cm
An art supplies shop sells three mathematically similar picture frames. The following information is known:
The frames are priced in direct proportion to their areas. Find:
(a) the price of the medium frame
(b) the length of the large frame.
Answer
(b) 45 cm
What is the volume of the smaller can?
Answer
Justify your answer.
Answer
A supermarket sells cylindrical cookie jars which are mathematically similar.
The smaller jar has a height of 15 centimetres and a volume of 750 cubic centimetres.
The larger jar has a height of 24 centimetres.
Calculate the volume of the larger jar.
Answer
The flag at each hole on a golf course is coloured red and blue.
The diagram below represents a flag.
Triangle QRT represents the red section.
PQTS represents the blue section.
Triangles PRS and QRT are mathematically similar.
The area of triangle QRT is 400 square centimetres.
Calculate the area of PQTS, the blue section of the flag.
Answer
Screenwash is available in bottles which are mathematically similar.
The smaller bottle has a height of 15 centimetres and a volume of 250 millilitres.
The larger bottle has a height of 36 centimetres.
Calculate the volume of the larger bottle.
Answer
A cinema sells popcorn in two different sized cartons.
The small carton is 16 cm deep and has a volume of 576 cubic centimetres.
The large carton is 24 cm deep and has a volume of 1125 cubic centimetres.
(a) Show that the two cartons are not mathematically similar.
(b) The large carton is redesigned so that the two cartons are now mathematically similar. The volume of the redesigned large carton is 1500 cubic centimetres. Calculate the depth of the redesigned large carton.
Answer
(b) 22 cm
The two photographs shown are mathematically similar.
The small photograph has an area of 80 square centimetres, and is 12 centimetres wide.
The large photograph has an area of 500 square centimetres.
Calculate the width of the large photograph.
Answer
In the diagram, triangles ABC and ADE are mathematically similar.
• BC = 3 centimetres
• DE = 7 centimetres
• AD = 10.5 centimetres
Calculate the length of BD.
Answer
Two model aircraft are mathematically similar.
The small model is 14 cm long, and the area of one wing is 24 cm². The large model is 31.5 cm long.
Calculate the area of one wing of the large model.
Answer
Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.