Which of the following lengths can be the side-lengths of a triangle? Class 7

Which of the following lengths can be the side-lengths of a triangle? Class 7

Question 1.

Which of the following lengths can be the side-lengths of a triangle? Explain your answers. Note that for each set, the three lengths have the same unit of measure. Class 7

(a) 2, 2, 5

(b) 3, 4, 6

(c) 2, 4, 8

(d) 5, 5, 8

(e) 10, 20, 25

(f) 10, 20, 35

(g) 24, 26, 28

Solution:

(a) Not possible because 2 + 2 < 5.

(b) Possible as 3 < 4 + 6, 4 < 3 + 6, 6 < 3 + 4.

(c) Not possible 2 + 4 < 8.

(d) Possible as 5 < 5 + 8, 8 < 5 + 5.

(e) Possible as 10 < 20 + 25, 20 < 10 + 25, 25 < 10+ 20.

(f) Not possible as 10 + 20 < 35.

(g) Possible as 24 < 26 + 28, 26 < 24 + 28, 28 < 24 + 26.

Question 2.

Will triangles always exist when a set of lengths satisfies the triangle inequality? How can we be sure? Class 7

Solution:

Yes. By actually constructing the triangle.