<u>Answer</u>:-
Q no.8 :
9, 13, 17 can merely be the correct option.
Explanation:-
• The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.
For instance:-
1) Calculation: 9 + 13 = 22 which is greater than the third side (the hypotenuse) that was 17. And hence is correct.
2) Calculation: 10 + 10 = 20 which is equal to the third/hypotenuse side that was also 20. Therefore it doesn’t fit the theorem and is unable to form a triangle.
3)Calculation: 6+8 = 14 which is less than the greatest/hypotenuse/third side or the side of measure 15. Thence, it isn’t the correct also. No accurate triangle can be formed from all these(6, 8, 15) measurements.
4) Calculation: 2+3 = 6 which is equal to the third /hypotenuse side of measure 6 also. And therefrom no triangle can be constructed from the given sides(2, 3, 6).
• The third important property of triangles is the triangle inequality rule, which states:
“The length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides”.
(Note: I honestly prefer you to understand from the first point which is far much clearer than the second one).
