Higher January 2019 Paper 1R Q21
21 Here is a triangle \(XYZ\).
Diagram NOT accurately drawn
The perimeter of the triangle is \(k\) cm.
Given that \(x = y - 1\)
find the value of \(k\).
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| \(x^2 = 5^2 + y^2 - 2 \times 5 \times y\cos 60^\circ\) | M1 |
| \((y - 1)^2 = 5^2 + y^2 - 5y\) or \(x^2 = 5^2 + (x + 1)^2 - 5x - 5\) | M1 |
| \(y^2 - 2y + 1 = 25 + y^2 - 5y\) or \(x^2 = 5^2 + x^2 + 2x + 1 - 5x - 5\) | M1 |
| \(5y - 2y = 25 - 1\) or \(y = 8\) or \(3x = 21\) or \(x = 7\) | M1 |
| 20 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: recognising need for the cosine rule
M1: for expansion of \((y - 1)^2\) or \((x + 1)^2\) in a correct equation
M1: for correct linear equation with correct isolation of terms