Intermediate November 2019 Unit 2 Q18
18. 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 |
|---|---|---|
| \(\dfrac{24 \times \text{AC}}{2}\) = 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 |