iGCSE Mathematics (0580) - C4.4 Similarity- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
Since the rectangles are mathematically similar, the ratio of their corresponding sides is exactly the same. We can find the linear scale factor from rectangle $B$ to rectangle $A$: $$\text{Scale Factor} = \frac{\text{Length of } A}{\text{Length of } B} = \frac{8}{2} = 4$$ This means rectangle $A$ is 4 times larger in every dimension. We apply this factor to the width: $$x = 1.5 \times 4 = 6$$
Answer: $x =$ 6
▶️ Answer/Explanation
Since the triangles are mathematically similar, their corresponding sides are proportional. We find the scale factor by dividing the known side of the larger triangle by its corresponding side on the smaller triangle: $\text{Scale Factor} = \frac{PQ}{AB} = \frac{10}{5} = 2$. Multiplying the corresponding side $BC$ by this scale factor gives $QR = 7 \times 2 = 14\text{ cm}$.
✅ Answer: $\frac{10}{5} \times 7 = 14$
✅ Answer: $\frac{10}{5} \times 7 = 14$
