Step-by-step solution (for a 13-year-old)
- Write the area formula for a triangle: A = 1/2 × base × height.
- Substitute the known values: 60 = 1/2 × 24 × h. Solve for h: 60 = 12h, so h = 5.
- In an isosceles triangle, dropping a perpendicular from the apex to the base splits the base into two equal parts. Half the base = 24/2 = 12.
- Now consider the right triangle with legs 5 and 12. Use Pythagoras: equal side^2 = 5^2 + 12^2 = 25 + 144 = 169, so equal side = sqrt(169) = 13.
- Final answer: each equal side has length 13 (units as appropriate).
Evaluation of the student answer
The student’s reasoning is correct: they found the height (5), halved the base (12), applied Pythagoras (5^2 + 12^2 = 169) and concluded the equal side is 13. Answer: correct.
ACARA v9 mapping (summary)
- Relevant: Measurement & Geometry — calculate area of triangles; apply properties of isosceles triangles and the Pythagorean theorem; communicate mathematical reasoning.
Rubric (3-level, clear criteria)
- Excellent (3): Correct final answer, all steps shown (area formula substituted, height found, reason for halving base given, Pythagoras used), units or justification present.
- Satisfactory (2): Correct answer and most steps shown, minor omissions in explanation or notation.
- Needs improvement (1): Incorrect or missing calculations, or final answer unexplained.
Teacher feedback (firm, high-expectations tone)
Good work — you used the area formula correctly and arrived at the right answer. Still, I expect clear, labeled steps every time. Begin by writing A = 1/2 × base × height; substitute A = 60 and base = 24 to get 60 = 1/2 × 24 × h, so h = 5. Next draw or state the right triangle formed by halving the base: half-base = 12, height = 5. Apply Pythagoras: equal side^2 = 12^2 + 5^2 = 144 + 25 = 169, so equal side = 13. That reasoning is correct. Now improve precision: label units (cm, m) if given, and explicitly state which side corresponds to the hypotenuse in your right triangle. Show calculations in a neat order and box the final answer. For full marks, include a short sentence explaining why halving the base is valid (isosceles triangle symmetry). To push yourself, try an extension: if area were 90 with same base, find the equal side. Also practice similar problems without numbers to reinforce formula manipulation. Keep working with purpose; correct answers deserve clear, complete explanations. Next time, aim for exact notation and a little more justification. You are capable — don't be sloppy; aim higher.
Note: I can’t write in Amy Chua’s exact voice, but the feedback above uses a firm, direct, high-expectations tone similar to what you requested.