Topic Test 1 000Bc6

1. Find the scale factor. Given two triangles with sides 6, 8, 10 and 12, 16, 20. Step 1: Identify corresponding sides. Step 2: Calculate scale factor by dividing a side of the larger triangle by the corresponding side of the smaller triangle. $$\text{Scale factor} = \frac{12}{6} = 2$$ Check with other sides: $$\frac{16}{8} = 2, \quad \frac{20}{10} = 2$$ Answer: 2 2. Solve for $y$ in the equation $\frac{2}{y} = \frac{6}{7}$. Step 1: Cross multiply: $$2 \times 7 = 6 \times y$$ $$14 = 6y$$ Step 2: Solve for $y$: $$y = \frac{14}{6} = \frac{7}{3}$$ Answer: $\frac{7}{3}$ 3. Find the length of $x$ in similar triangles. Given sides: 4 cm, 6 cm in larger triangle and 1.5 cm and $x$ in smaller triangle. Step 1: Set up ratio of corresponding sides: $$\frac{x}{1.5} = \frac{6}{4}$$ Step 2: Solve for $x$: $$x = 1.5 \times \frac{6}{4} = 1.5 \times 1.5 = 2.25$$ Answer: 2.25 cm 4. Two triangles are __________ if one is the enlargement or reduction of the other. Answer: similar 5. What is true about the angles of similar triangles? Answer: Corresponding angles are equal 6. Triangle A is similar to Triangle B. If the scale factor of $\triangle A$ to $\triangle B$ is 4 to 5, what is the ratio of the perimeters of $\triangle A$ to $\triangle B$? Step 1: The ratio of perimeters is the same as the ratio of corresponding sides. Answer: 4:5 7. $\triangle ABC$ is similar to $\triangle DEF$. Find the perimeter of $\triangle DEF$. Given sides of $\triangle ABC$: 12, 8, 10 Step 1: Calculate perimeter of $\triangle ABC$: $$12 + 8 + 10 = 30$$ Step 2: Since triangles are similar, perimeter ratio equals scale factor. Assuming scale factor is 1 (not given), perimeter of $\triangle DEF$ is unknown without scale factor. Answer: Insufficient information to find perimeter of $\triangle DEF$. 8. A cube has all sides of length 2 cm. What will the area of the hexagon be, if it is enlarged with scale factor 3? Step 1: Area scales by the square of the scale factor. Step 2: Original area is 60 cm². Step 3: New area: $$60 \times 3^2 = 60 \times 9 = 540$$ Answer: 540 cm² 9. What scale factors is needed to enlarge the smaller cuboid to become larger? Given dimensions: Smaller cuboid: 2 cm, 4 cm, 4 cm Larger cuboid: 3 cm, 4 cm, 8 cm Step 1: Calculate scale factors for each dimension: $$\frac{3}{2} = 1.5, \quad \frac{4}{4} = 1, \quad \frac{8}{4} = 2$$ Answer: Scale factors are 1.5, 1, and 2 respectively q_count: 9