Answer :

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The correct option is option( A).

Using the property of Obtuse Triangle, the triangle with sides { 8, 10, 14 } is an Obtuse Triangle.

Obtuse Triangle:

An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In geometry, a triangle is represented as a closed 2D figure with three sides of equal or unequal length and three angles of equal or unequal measurements.

Obtuse triangle property:

  • The longest side of the triangle is opposite the obtuse angle.
  • A triangle can have only one obtuse angle.
  • The sum of the other two angles of an obtuse triangle is always less than 90°.
  • In an obtuse triangle, the sum of the squared lengths of the two short sides is less than the squared length of the longest side.

we have given the sides of triangle so, we use the fourth property for check the triangle formed by given sides are obtuse triangle or not .

8² + 10² = 164; 14² = 196 -> obtuse

9² + 12² = 225; 15² = 225 -> not obtuse

10² + 14²= 296 ; 17²= 289 --> not obtuse

12² + 15² = 369; 19²= 361 --> not obtuse

Hence, the required triangle is triangle with sides 8, 10, 14.

To learn more about Obtuse Triangle, refer:

https://brainly.com/question/3250447

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Complete Question:

which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle

A. 8, 10, 14

B. 9, 12, 15

C. 10, 14, 17

D. 12, 15, 19

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