Answer :
2,2,3 (C) and 3,5,6 (E) are the correct answers. The squares of 2 of their sides are less that that of the third side.
The given triangle whose sides are (4, 7, 8), (2, 2, 3) and (3, 5, 6) is an obtuse triangle and it can be determine by using pythagorian theorem.
Given :
The side lengths of a triangle are: 6cm, 10cm, and 12cm.
To determine that the sets of three of numbers represent the sides of an obtuse triangle, pythagorian theorem can be use. In pythagorian theorem, the square of the third side is equal to the sum of the square of shorter side of the right angle triangle. That is:
[tex]\rm (H)^2=(P)^2+(B)^2[/tex]
The condition of an obtuse triangle is: [tex]\rm (P)^2+(B)^2<(H)^2[/tex].
- Applying the condition of an obtuse triangle in option A): [tex]4^2+7^2 = 65[/tex] which is less than [tex]8^2[/tex]. Therefore option A) represents obtuse triangle.
- Applying the condition of an obtuse triangle in option B): [tex]3^2+4^2 = 25[/tex] which is equal to [tex]5^2[/tex]. Therefore option B) does not represents an obtuse triangle.
- Applying the condition of an obtuse triangle in option C): [tex]2^2+2^2 = 8[/tex] which is less than [tex]3^2[/tex]. Therefore option C) represents obtuse triangle.
- Applying the condition of an obtuse triangle in option D): [tex]6^2+8^2 = 100[/tex] which is greater than [tex]9^2[/tex]. Therefore option D) does not represents obtuse triangle.
- Applying the condition of an obtuse triangle in option E): [tex]3^2+5^2 = 34[/tex] which is less than [tex]6^2[/tex]. Therefore option E) represents obtuse triangle.
Therefore, it can be concluded that option A), C), and E) represents an obtuse triangle.
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