iGCSE Mathematics (0580) - C4.4 Similarity- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
For mathematically similar shapes, the ratio of corresponding side lengths is constant. We set up a ratio connecting the known sides.
$\frac{AB}{12} = \frac{42}{28}$
$AB = 12 \times (\frac{42}{28})$
$AB = 12 \times 1.5 = 18$
✅ Answer: 18
▶️ Answer/Explanation
(a)
Since the geometric shapes match proportionally, we can set up equal scaling fractions: $\frac{20.8}{x} = \frac{9.1}{1.4}$.
Cross-multiplying to rearrange gives the equation: $9.1x = 20.8 \times 1.4$.
$9.1x = 29.12$, which simplifies to $x = 3.2\text{ cm}$.
✅ Answer: 3.2
(b)
Using basic right-angled trigonometry ratios, we choose the cosine function because it links the adjacent side to the hypotenuse: $\cos(38^{\circ}) = \frac{y}{5.4}$.
Isolating our unknown variable gives: $y = 5.4 \times \cos(38^{\circ})$.
Evaluating this product expression gives $y \approx 4.26\text{ cm}$.
✅ Answer: 4.26 (or 4.255…)