Check if a triangle exists for each of the following set of lengths: Class 7

Check if a triangle exists for each of the following set of lengths: Class 7

Question 1.

Check if a triangle exists for each of the following set of lengths : Class 7

(a) 1, 100, 100

(b) 3, 6, 9

(c) 1, 1, 5

(d) 5, 10, 12

Solution:

(a) exists,

(b) does not exist,

(c) does not exist,

(d) exists.

Question 2.

Does there exist an equilateral triangle with sides 50, 50, 50? In general, does there exist an equilateral triangle of any side-length? Justify your answer. Class 7

Solution:

Yes. Yes.

Do as directed. (Sum of two sides will always be greater than the third side.)

Question 3.

For each of the following, give at least 5 possible values for the third length so there exists a triangle having these as sidelengths (decimal values could also be chosen): Class 7

(a) 1, 100

(b) 5, 5

(c) 3, 7

Solution:

(a) 101, 102, 103, 104, 105

(b) 5.5, 6, 7, 8, 9.5

(c) 5, 6, 7, 8.5, 9