We checked by construction that there are no triangles having side lengths. Class 7
mediumWe checked by construction that there are no triangles having side lengths. Class 7
Question 1.
We checked by construction that there are no triangles having side lengths 3 cm, 4 cm and 8 cm; and 2 cm, 3 cm and 6 cm. Check if you could have found this without trying to construct the triangle. Class 7
Solution:
Do as directed.
3 + 4 < 8;
2 + 3 < 6.
Question 2.
Can we say anything about the existence of a triangle for each of the following sets of lengths?
(a) 10 km, 10 km and 25 km
(b) 5 mm, 10 mm and 20 mm
(c) 12 cm, 20 cm and 40 cm
You would have realised that using a rough figure and comparing the direct path lengths with their corresponding roundabout path lengths is the same as comparing each length with the sum of the other two lengths. There are three such comparisons to be made. Class 7
Solution:
(a) Not exist
(b) Not exist
(c) Not exist
Question 3.
Will this always happen? That is, for any set of lengths, will there be at least two comparisons where the direct length is less than the sum of the other two? Explore for different sets of lengths. Class 7
Solution:
No. For example, in the set of lengths 10 cm, 10 cm, 25 cm, there is only one comparison 10 cm < (10 + 25) cm, where direct length is less than the sum of the other two. It will only in the case when two of the three lengths are equal.