Respuesta :
Option (C) 2, (D) 3, (E) 6, (F) 10 are all possible side length for the third side of the triangle.
What is a triangle?
A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
The sides of the triangle are 5 inches and 7 inches.
According to triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side.
⇒ [tex]5+7=12[/tex]
⇒ [tex]7-5=2[/tex]
Let the third side be x.
The third side should be in the range from [tex]2 < = x < = 12.[/tex]
So options C, D, E, F are possible.
Option C:
Let x = 2,
⇒ [tex]2+5 > =7[/tex]
⇒ [tex]7 > =7[/tex]
Option D:
Let x = 3,
⇒ [tex]3+5 > 7[/tex]
⇒ [tex]8 > 7[/tex]
Option E:
Let x = 6,
⇒ [tex]6+5 > 7[/tex]
⇒ [tex]11 > 7[/tex]
Option F:
Let x = 10,
⇒ [tex]10+5 > 7[/tex]
⇒ [tex]15 > 7[/tex]
Hence we can conclude that option (C) 2, (D) 3, (E) 6, (F) 10 are all possible side length for the third side of the triangle.
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