which one of the following cannot be the sides of the triangle?
(a) 4,5,6
(b) 3,4,5
(c) 2,3,4
(d) 1,2,3
Answers
1 , 2 , 3 can not be the sides of a Triangle
Step-by-step explanation:
Property of triangle
Sum of any two sides > third Side
4 , 5 , 6
4 + 5 > 6 , 4 + 6 > 5 , 5 + 6 > 4
3 , 4 , 5
3 + 4 > 5 , 3 + 5 > 4 , 4 + 5 > 3
2 , 3 , 4
2 + 3 > 4 , 2 + 4 > 3 , 3 + 4>2
1 , 2 , 3
1 + 2 = 3
Sum of 1 & 2 is not greater than 3
Hence these can not be the sides of a Triangle
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The measurements 1, 2, 3 cannot be the sides of the triangle.
- We know that, in a triangle
sum of lengths of two sides > length of third side
- From the given options, options (a), (b), (c) satisfy this property.
- Hence, they can be sides of a triangle.
- Consider option (d). In this case,
2 + 3 = 5>1
1 + 3 = 4 > 2
But,
1 + 2 = 3 = 3 ( third side)
∴ They cannot form the sides of the triangle.
Option (d) is the correct answer.