Question : The ratio of the three sides of the triangle is 5 : 13 : 12. What is the largest angle of the triangle?
Option 1: 80°
Option 2: 90°
Option 3: 135°
Option 4: 120°
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Correct Answer: 90°
Solution : Given: The ratio of the three sides of the triangle is 5 : 13 : 12. The ratio of the three sides of the triangle forms Pythagoras triplets. Let the sides of the triangle be $x$. According to the question, $(5x)^2+(12x)^2$ = $25x^2+144x^2$ = $169x^2$ = $(13x)^2$ So, the ratio of the three sides of the triangle forms Pythagoras triplets. Therefore, the triangle is a right-angled triangle. Thus, the largest angle of the triangle = 90°. Hence, the correct answer is 90°.
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