Answer with explanation:
A triangle is valid triangle if sum of length of two sides is greater than the third side.
Let one side =a = 3 cm
Second side =b = 5 cm
Third Side = c Cm
So, for a valid triangle
1.
a+b > c
3 +5 > c
c < 8 Cm
2.
c+3 > 5
c> 5-3
c>2 Cm
3.
As, 5+c will always be greater than 3.
→→→So, combining 1 and 2 , we get
2 Cm< Third side < 8 Cm, for a valid triangle.
Third side to construct a valid triangle in which two side of 3 cm and 5 centimetre should be between 2 cm to 8 cm.
Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater then the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b)>c
(b+c)>a
(c+a)>b
The one side length of the triangle is 3 centimetres.
The another side length of the triangle is 5 centimetres.
The length of the third side to construct a valid triangle has to be find out for which the two side lengths of 3 centimetres and 5 centimetres is given.
Let the third side of the triangle is x centimetres. Thus by the triangle inequality theorem, for first two sides as 3 and 5,
[tex](3+5)>x\\8>x[/tex]
Similarly, the sides 3 and x can be given as,
[tex](3+x)>5\\x>5-3\\x>2[/tex]
Thus, the third side to construct a valid triangle for which the two side lengths of 3 centimetres and 5 centimetres should be between 2 cm to 8 cm.
Learn more about the triangle inequality theorem here;
https://brainly.com/question/26037134
