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Are these two triangles mathematically similar? Show how you decide - OCR - GCSE Maths - Question 25 - 2019 - Paper 1

Question 25

Are these two triangles mathematically similar? Show how you decide. 6 cm 10 cm 11 cm 15 cm Not to scale

Worked Solution & Example Answer:Are these two triangles mathematically similar? Show how you decide - OCR - GCSE Maths - Question 25 - 2019 - Paper 1

Step 1

Determine the side lengths of each triangle

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Answer

The first triangle has side lengths of 6 cm, 10 cm, and the hypotenuse can be found using the Pythagorean theorem:
$c = \sqrt{(6^2 + 10^2)} = \sqrt{(36 + 100)} = \sqrt{136} \approx 11.66 \text{ cm}$
The second triangle has side lengths of 11 cm, 15 cm, and the hypotenuse can be calculated as follows:
$c = \sqrt{(11^2 + 15^2)} = \sqrt{(121 + 225)} = \sqrt{346} \approx 18.6 \text{ cm}$

Step 2

Calculate the ratio of corresponding sides

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Answer

For the first triangle, the ratios of the sides are:

Ratio of the first triangle's shorter side (6 cm) to the second triangle's shorter side (11 cm):
$\frac{6}{11}$
Ratio of the first triangle's other side (10 cm) to the second triangle's other side (15 cm):
$\frac{10}{15} = \frac{2}{3}$

Step 3

Compare the ratios

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Answer

Since the ratios (\frac{6}{11}) and (\frac{2}{3}) are not equal, the triangles are not mathematically similar.
Therefore, we conclude that:
These triangles are not similar because the ratios of their corresponding sides are not equal.

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