Higher November 2019 Paper 2 Q12
12 An isosceles triangle has base 16 cm and perpendicular height 15 cm
Not drawn accurately
Some of these triangles are used to make a large triangle.
Not drawn accurately
Work out the perimeter of the large triangle. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(15^2\) or 225 and \((16 \div 2)^2\) or \(8^2\) or 64 | M1 | oe |
| \(\sqrt{15^2 + (16 \div 2)^2}\) or \(\sqrt{\text{their } 225 + \text{their } 64}\) or \(\sqrt{289}\) or 17 | M1dep | oe full trigonometric method leading to 17 scores M2 eg \(\dfrac{15}{\sin\left(\tan^{-1}\dfrac{15}{8}\right)}\) |
| \(6 \times\) their \(17 + 3 \times 16\) or \(102 + 48\) | M1dep | oe |
| 150 | A1 | SC2 \(48 + 6\sqrt{161}\) or [124.08, 124.2] |
| Alternative method 2 | ||
| \((48 \div 2)^2\) or \(24^2\) or 576 and \((15 \times 3)^2\) or \(45^2\) or 2025 | M1 | oe eg \((16 \times 1.5)^2\) and \((3 \times 15)^2\) |
| \(\sqrt{(48 \div 2)^2 + (3 \times 15)^2}\) or \(\sqrt{\text{their } 576 + \text{their } 2025}\) or \(\sqrt{2601}\) or 51 | M1dep | oe full trigonometric method leading to 51 scores M2 eg \(\dfrac{45}{\sin\left(\tan^{-1}\dfrac{15}{8}\right)}\) or \(\dfrac{45}{\sin\left(\tan^{-1}\dfrac{45}{24}\right)}\) |
| \(2 \times\) their \(51 + 3 \times 16\) or \(102 + 48\) | M1dep | oe |
| 150 | A1 | SC2 \(48 + 6\sqrt{161}\) or [124.08, 124.2] |
Additional guidance
| \(15^2 - 8^2\) or \(45^2 - 24^2\) | M1M0M0A0 (unless SC2 scored) |
| Allow 61.9(2…) or 61.93 or 62 for \(\tan^{-1}\dfrac{15}{8}\) but do not award A1 if premature approximation seen |