18.5 Similarity and similar lengths — Practise

1. Similar shapes have corresponding sides $4$ cm and $10$ cm. Find the scale factor from small to large.

Answer: 5/2

2. Similar triangles have sides $3,4,5$ and a corresponding longest side $15$. Find the scale factor and the other two sides.

Answer: Scale factor $3$; sides $9$ and $12$.

3. Two similar rectangles have corresponding widths $5$ cm and $8$ cm. A short side of the first is $3$ cm. Find the corresponding side.

Answer: 4.8 cm

4. Are triangles with sides $2,3,4$ and $4,6,8$ similar? Give a reason.

Answer: Yes; each corresponding side has scale factor $2$.

5. Corresponding sides are $7$ cm and $21$ cm. A second side on the smaller shape is $5$ cm. Find its matching length.

Answer: 15 cm

6. A model bridge is $1.2$ m long. The real bridge is $30$ m long. Find the scale factor from model to real.

Answer: 25

7. Two similar shapes have scale factor $1.4$. Are they congruent? Explain.

Answer: No; congruent shapes have scale factor $1$.

8. Similar triangles have corresponding sides $8$ and $12$. A side matching $10$ is on the second triangle. Find its corresponding side on the first.

Answer: 20/3

9. A drawing uses scale $1:50$. A line is $6$ cm on the drawing. Find the real length in metres.

Answer: 3 m

10. Lengths $6,9,12$ are compared with $10,15,20$. Which method checks similarity, and why?

Answer: Compare corresponding ratios; all are $5/3$, so the shapes are similar.