Mathematics • Year 7 • Unit 3 • Lesson 16
Similar Figures — Real World
Apply similarity to real situations: enlarging photos, scaling drawings, building models. The same rule applies every time — corresponding sides share ONE scale factor.
1. Word problems
Each problem needs you to identify the corresponding sides, compute the scale factor, and answer the question. Show your working — a single answer with no working only earns half marks.
1.1 — Phone photo to poster. A photo on a phone screen is 6 cm wide and 9 cm tall. It is enlarged to make a poster that is 24 cm wide.
(a) Find the scale factor from photo to poster.
(b) Find the height of the poster. 2 marks
1.2 — Toy car model. A toy car is a similar (scaled-down) copy of a real car. The toy is 14 cm long and the real car is 420 cm long.
(a) Find the scale factor from REAL car to TOY car.
(b) The toy car has wheels of diameter 1.5 cm. What is the diameter of the real car's wheels, in cm? 3 marks
1.3 — School flag. A small school flag is a 30 cm × 45 cm rectangle. The school orders a banner that is similar to the flag and 90 cm wide.
(a) Find the scale factor from flag to banner.
(b) Find the height of the banner. 2 marks
1.4 — Tile design. A triangular floor tile has sides 12 cm, 18 cm and 24 cm. A larger similar tile is to be made with shortest side 30 cm.
(a) Find the scale factor from small to large tile.
(b) Find the other two side lengths of the large tile. 3 marks
1.5 — Identifying similar shapes. Maya has FOUR rectangles. Rectangle W is 4 cm × 6 cm. Rectangle X is 8 cm × 12 cm. Rectangle Y is 6 cm × 9 cm. Rectangle Z is 8 cm × 10 cm.
Which of X, Y and Z is/are similar to W? Justify each one by checking ratios. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate looks at a 5 cm × 7 cm rectangle and a 10 cm × 12 cm rectangle. They say: "Both rectangles got bigger by 5 cm in width and 5 cm in length, so they must be similar." In your own words, explain (i) why your classmate is wrong, (ii) what similarity actually requires of corresponding sides, and (iii) what the larger rectangle's length WOULD have to be (in cm) for the two rectangles to be genuinely similar.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Phone photo to poster
(a) SF = 24 ÷ 6 = 4.
(b) Poster height = 9 × 4 = 36 cm.
1.2 — Toy car model
(a) SF (real → toy) = 14 ÷ 420 = 1/30. (The toy is one-thirtieth the size.)
(b) Going the other way (toy → real), multiply by 30: real wheel diameter = 1.5 × 30 = 45 cm.
1.3 — School flag
(a) SF = 90 ÷ 30 = 3.
(b) Banner height = 45 × 3 = 135 cm.
1.4 — Tile design
(a) SF = 30 ÷ 12 = 2.5.
(b) Other sides = 18 × 2.5 = 45 cm and 24 × 2.5 = 60 cm.
1.5 — Similar rectangles
W is 4 × 6 — its ratio of short to long is 4 : 6 = 2 : 3.
X (8 × 12): ratios 8 ÷ 4 = 2, 12 ÷ 6 = 2 — both match. Similar to W (SF = 2). ✓
Y (6 × 9): ratios 6 ÷ 4 = 1.5, 9 ÷ 6 = 1.5 — both match. Similar to W (SF = 1.5). ✓
Z (8 × 10): ratios 8 ÷ 4 = 2, 10 ÷ 6 ≈ 1.67 — different. NOT similar to W. ✗
2.1 — Explain your thinking (sample response)
My classmate is wrong because similarity is about ratios, not differences. Just because both sides increased by 5 cm doesn't mean the shapes are similar. The original rectangle 5 × 7 has ratio 5 : 7. The new rectangle 10 × 12 has ratio 10 : 12 = 5 : 6. Because 5 : 7 ≠ 5 : 6, the rectangles are NOT similar. For similar figures, every pair of corresponding sides has to share the SAME scale factor (new ÷ old). Here 10 ÷ 5 = 2 but 12 ÷ 7 ≈ 1.71 — different ratios. For the rectangles to be genuinely similar, the larger length would have to be 7 × 2 = 14 cm, making it a 10 × 14 rectangle with SF = 2 throughout.
Marking: 1 for identifying ratios vs differences; 1 for correctly stating equal ratios are required; 1 for showing the actual ratios differ; 1 for correct answer of 14 cm.