Higher November 2019 Unit 2 Q9
9. The right-angled triangle \(ABC\) has an area of 84 cm2.
\(AB\) = 24 cm.
Diagram not drawn to scale
Calculate the perimeter of the triangle \(ABC\).
You must show all your working. [6]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{24 \times AC}{2} = 84\) or equivalent. | M1 | |
| AC = 7 (cm) | A1 | |
| (BC2 =) 72 + 242 | M1 | F.T. ‘their AC’. |
| BC2 = 625 or (BC =) √625 | A1 | Final answer of BC = 625 is M1A0A0. |
| (BC =) 25(cm) | A1 | F.T. √’their 625’ provided M1 gained. |
| (Perimeter = 24 + 7 + 25 =) 56(cm) | B1 | F.T. 24 + ‘their AC’ + ‘their BC’ provided at least one M1 mark gained AND ‘their BC’ > 24. |
Alternative method to find BC
A correct and complete method (e.g.using two trigonometric relationships.) M2
BC = 25(cm) A1