Success Homeschool

Year 10 Mathematics · Similar figures and scale

Name: ______________________

Date: ____________

1. Which of these pairs are ALWAYS similar?
- ☐ (a) Any two rectangles
- ☐ (b) Any two squares
- ☐ (c) Any two triangles
- ☐ (d) Any two parallelograms
2. A side of 5 cm is enlarged to 15 cm. What is the scale factor?
- ☐ (a) 3
- ☐ (b) 10
- ☐ (c) 13
- ☐ (d) 5
3. On a map with scale 1 : 25 000, what real distance does 4 cm represent?
- ☐ (a) 1 km
- ☐ (b) 100 m
- ☐ (c) 10 km
- ☐ (d) 4 km
4. In similar figures, matching angles are:
- ☐ (a) multiplied by the scale factor
- ☐ (b) equal
- ☐ (c) supplementary
- ☐ (d) always 90°
5. Two triangles are similar. The smaller has sides 4 cm, 6 cm and 8 cm. The shortest side of the larger triangle is 10 cm. How long is the longest side of the larger triangle?
6. A 1.2 m stick casts a 1.6 m shadow. At the same time, a building casts a 20 m shadow. How tall is the building, in metres?
7. A floor plan has a scale of 1 : 200. A room is 3.5 cm long on the plan. How long is the real room, in metres?
8. A model car is built to a scale of 1 : 18. The real car is 4.5 m long. How long is the model, in centimetres?

Answer sheet

1. Any two squares — All squares have 90° angles and four equal sides, so one is always an enlargement of the other. Rectangles, triangles and parallelograms can have different shapes.
2. 3 — Scale factor = image ÷ original = 15 ÷ 5 = 3.
3. 1 km — 4 × 25 000 = 100 000 cm = 1000 m = 1 km.
4. equal — An enlargement changes lengths but not angles, so matching angles are equal.
5. 20 cm — Scale factor = 10 ÷ 4 = 2.5. Longest side = 8 × 2.5 = 20 cm.
6. 15 m — Scale factor = 20 ÷ 1.6 = 12.5. Height = 1.2 × 12.5 = 15 m.
7. 7 m — 3.5 × 200 = 700 cm = 7 m.
8. 25 cm — 4.5 m = 450 cm. Model length = 450 ÷ 18 = 25 cm.