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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