Intermediate November 2021 Unit 2 Q13
13. Show that the triangle below is not a right-angled triangle. [5]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| 5x − 17 + 2x + 9 + x + 20 = 180 | M1 | |
| 8x = 168 | A1 | |
| x = 21 | A1 | F.T. from ax = b. Allow all 3 marks for x = 21. |
| Substituting x = 21 into at least one expression. | M1 | If x ≠ 21 FT ‘their derived value of x’. |
| (5x – 17 =) 88(°) (2x + 9 =) 51(°) (x + 20 =) 41(°) (So not a right-angled triangle) | A1 | F.T. for this A1 if x ≥ 4. Any two of these expressions correctly evaluated with no incorrect evaluation, provided the sum of the two found is > 90. (statement not required). Note If further work indicates that the values found are not treated as angles (e.g. showing 512 +412 ≠ 882) then award final M0A0. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 5x − 17 = 90 OR 2x + 9 = 90 OR x + 20 = 90 | M1 | |
| x = 21·4 AND x = 40·5 AND x = 70 | A2 | Award A1 for any one of these: x = 21·4 OR x = 40·5 OR x = 70 |
| Then verifying: If x = 21·4: 5x − 17 + 2x + 9 + x + 20 = 183.2 AND If x = 40·5: 5x − 17 + 2x + 9 + x + 20 = 336 AND If x = 70: 5x − 17 + 2x + 9 + x + 20 = 572 (So not a right-angled triangle) | A2 | Award A1 for any one of these: If x = 21·4: 5x − 17 + 2x + 9 + x + 20 = 183.2 OR If x = 40·5: 5x − 17 + 2x + 9 + x + 20 = 336 OR If x = 70: 5x − 17 + 2x + 9 + x + 20 = 572 |