Higher November 2019 Paper 1 Q14
14 The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 27.5 cm\(^2\)
Work out the length of the shortest side of the triangle.
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 5 | P1 | for process to find the area of the triangle, eg. \(0.5 \times (x + 4)(x - 2)\) oe OR for process to find the area of rectangle and \(27.5 \times 2\), eg. \((x + 4)(x - 2)\) and 55 |
| P1 | (dep P1) for process to expand the brackets and derive a quadratic equation, eg. \(x^2 + 4x - 2x - 8 = 55\) or \(0.5(x^2 + 4x - 2x - 8) = 27.5\) oe | |
| P1 | (dep P2) for complete process to solve the quadratic equation \(x^2 + 2x - 63 = 0\) eg \((x - 7)(x + 9)\ (= 0)\) or \(\dfrac{-2 \pm \sqrt{2^2 - 4 \times 1 \times -63}}{2 \times 1}\) or \((x + 1)^2 - 1 - 63\ (= 0)\) | |
| A1 | cao | |
| SC: B1 for \(x^2 + 4x - 2x - 8 = 27.5\) |
Additional guidance
Trial and improvement methods must be fully correct identifying the value of \(x\) as 7 (3 marks) or the shortest side as 5 (4 marks)
An answer of 5 with no supportive working gets no marks