Answer:
C
D
1,2,3,4,5,6 And 7
Explanation:
1. By the nature of triangles, the sum of the two sides has to be greater than the third and the difference between two sides has to be less than the third side.
A. 5+6=11 Wrong
B. 1+3<5 Wrong
C. 5+16>20 Right
16-5<20
D.7+7=14 Wrong
2. Two sides of a Triangle are 15 and 8
A. 8+9>15 15-8<9 Can
B. 8+13>15 15-8<13 Can
C. 15+8>21 21-8<15 Can
D. 15+8<25 Cannot
3. According to the Trilateral Relation of Triangle
Let's say the length of the third side is X (X≠Z)
i. 4-4<x x>8 0<X>8 (X≠Z)
4-4>x x<8
i. In 0,1,2,3,4,5,6,7,8,9,10
X could be 1,2,3,4,5,6, and 7
TRIANGLE
A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon.
Each triangle has three sides and three angles, with some of the angles being the same.
In the case of a right triangle, the side opposite the right angle is known as the hypotenuse, while the other two sides are known as the legs.
Trilateral Relationship of Triangle
A trilateral is a shape with three sides in geometry. 'Of trilateral figures, an equilateral triangle is one with three equal sides, an isosceles triangle is one with two equal sides, and a scalene triangle is one with three unequal sides.'
Triangle Inequality
The triangle inequality asserts that the sum of the lengths of any two sides of a triangle must be larger than or equal to the length of the remaining side in mathematics.
The condition of the triangle's sides
According to the triangle inequality, the lengths of any two triangle sides must be more than or equal to the length of the third side. Only a degenerate triangle with collinear vertices can have that total equal to the length of the third side.
If and only if the side lengths satisfy the triangle inequality, a triangle with three given positive side lengths exists.