Higher June 2024 Paper 1 Q19
19
\(ABC\) and \(DAB\) are similar isosceles triangles.
\(AB = AC\)
\(AD = BD\)
\(BC : CD = 4 : 21\)
Find the ratio \(AB : AD\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 2 : 5 | P1 | for using similar triangles to form an equation eg \(\dfrac{AB}{BC} = \dfrac{AD}{AB}\) oe or \(\dfrac{AB}{4} = \dfrac{25}{AB}\) oe or \(\dfrac{AB}{4k} = \dfrac{25k}{AB}\) oe or \(AB : 4 = 25 : AB\) oe or \(BC \times \text{sf} = BD \div \text{sf}\) oe or \(4 \times \text{sf} = 25 \div \text{sf}\) oe or for working with the perpendicular height of triangle \(ABC\) eg \((h^2 =)\ 25^2 - 23^2\ (= 96)\) or \((h =)\ \sqrt{25^2 - 23^2}\ (= \sqrt{96})\) |
| P1 | for process to find \(AB\) eg \((AB =)\ \sqrt{4 \times 25}\ (= 10)\) oe or \(\sqrt{\text{``}96\text{''} + 2^2}\ (= 10)\) or for process to find the scale factor eg \(\sqrt{\dfrac{25}{4}}\ \left(= \dfrac{5}{2} \text{ oe}\right)\) | |
| A1 | oe |
Additional guidance
May use \(x\) or any other letter for \(AB\)
Accept \(AB = 4 \times \text{sf}\), \(AB = 25 \div \text{sf}\)