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ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 9 - 2019 - Paper 3
Question 9
ABC is a right-angled triangle. Here is Sarah's method to find the length of BC. BC² = AB² + AC² = 6² + 8² = 100 BC = 10 (a) What mistake has Sarah made in her me... show full transcript
Worked Solution & Example Answer:ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 9 - 2019 - Paper 3
Step 1
What mistake has Sarah made in her method?
Answer
Sarah made an error in applying the Pythagorean theorem. Specifically, she incorrectly used addition instead of correctly applying the theorem. For a right-angled triangle,
the relationship should be as follows:
She should have calculated:
This part is correct. However, the mistake is in using the results of Pythagorean addition while interpreting the square root of the final result. She should have calculated:
Her understanding might be that she's adding areas which could lead to the wrong conclusion if interpreted differently.
Step 2
Explain why Roy's diagram is not correct.
Answer
Roy's diagram is incorrect because he used the wrong scale factor for enlargement. He intended to use a scale factor of ( \frac{1}{2} ), meaning each side length of triangle PQR should be halved. Instead, he may have either miscalculated the lengths or inaccurately represented them in his diagram. This discrepancy results in triangle XYZ not being a true half-sized representation of triangle PQR, leading to distortion of the shapes and dimensions.