Student solution checked
Given: base = 24, area = 60. Student's steps:
- Use area formula: area = 1/2 × base × height. So 60 = 1/2 × 24 × h ⇒ h = 5. (Correct.)
- Half the base = 12 (because an isosceles triangle split down the middle gives two right triangles). (Correct.)
- Apply Pythagoras to the right triangle with legs 5 and 12: 5^2 + 12^2 = 25 + 144 = 169. √169 = 13. So the equal side = 13. (Correct.)
Final answer: 13 (units).
Evaluation of the student answer
- Correctness: Correct — final answer 13 is right.
- Method: Appropriate and efficient — used area to get height, then Pythagoras.
- Arithmetic: Accurate.
- Presentation: Clear; could be slightly improved by explicitly showing the substitution step for the area (60 = 1/2 × 24 × h) and by including units.
Suggested short improvement
Add one line: 60 = (1/2)(24)h ⇒ 60 = 12h ⇒ h = 5. Then mention units if given (e.g. cm).
Rubric (simple, for marking)
- Excellent (4): Correct result, clear steps (area substitution shown), correct reasoning that halves the base, units given.
- Good (3): Correct result and method, minor missing detail (e.g. didn’t show the area substitution step explicitly).
- Developing (2): Correct idea but arithmetic or reasoning incomplete or unclear.
- Emerging (1): Method missing or incorrect; answer incorrect.
ACARA v9 alignment
Aligned to Year 8 Measurement and Geometry expectations: use and manipulate area formulas for triangles and apply the Pythagorean theorem to find unknown side lengths in right-angled triangles; demonstrate procedural fluency and reasoning.
Teacher comment (Nigella Lawson cadence)
Oh, what a delight to open your work and find such tidy thinking — exact, confident and altogether satisfying. You began by coaxing the height from the area, a simple rearrangement of the formula that produced h = 5, like a perfect little rise from the oven. You then bisected the base into two neat twelves, creating a right-angled triangle ready for the Pythagorean flourish. Squaring twelve yields 144; squaring five yields 25; you folded them together to make 169 and, with the small, elegant gesture of a square root, revealed 13. The arithmetic is immaculate and your method economical — no unnecessary fuss, just steady, correct steps. For the next time, a tiny garnish would make your solution irresistible: show the substitution explicitly (60 = 1/2 × 24 × h ⇒ h = 5) and label units if they’re part of the problem. Also, a quick note about why the triangle splits into right triangles — a one-line explanation or a little sketch — would make your reasoning perfectly plated for any examiner. Overall, this is a correct, well-presented solution: logical, efficient and beautifully neat. Keep serving your mathematics with this same care and clarity.