If in any triangle, the angles are in the ratio of 1 : 2 : 1, then what will be the ratio of its sides?
Answer & explanation
Correct answer: option 4
Ratio of angles of triangle,
1 : 2 : 1
Ratio = a : 2a : a
According to the question,
⇒ a + 2a + a = \({180}^\circ\)
⇒ 4a = \({180}^\circ\)
⇒ a = \({45}^\circ\)
⇒ 2a = \({90}^\circ\)
Therefore, it is a right angled triangle,
Let AB + BC = b cm
⇒ \( { (AC)}^{2 } \) = \( { (AB)}^{2 } \) + \( { (BC)}^{2 } \)
⇒ \( { (AC)}^{2 } \) = \( { 2b}^{2 } \)
⇒ AC = b\(\sqrt {2 }\)
⇒ Ratio of AB : AC : BC = b : b\(\sqrt {2 }\) : b = 1 : \(\sqrt {2 }\) : 1